Precache the next entry in your playlist if it is a network source by downloading it to a temp file ahead of time. Change Line 20 to temp directory. It will delete the directory on exit.

ytdl-preload.lua

----------------------
-- #example ytdl_preload.conf
-- # make sure lines do not have trailing whitespace
-- # ytdl_opt has no sanity check and should be formatted exactly how it would appear in yt-dlp CLI, they are split into a key/value pair on whitespace
-- # at least on Windows, do not escape '\' in temp, just us a single one for each divider

-- #temp=R:\ytdltest
-- #ytdl_opt1=-r 50k
-- #ytdl_opt2=-N 5
-- #ytdl_opt#=etc
----------------------
local nextIndex
local caught = true
-- local pop = false
local ytdl = "yt-dlp"
local utils = require 'mp.utils'

local options = require 'mp.options'
local opts = {
    temp = "R:\\ytdl",
    ytdl_opt1 = "",
    ytdl_opt2 = "",
    ytdl_opt3 = "",
    ytdl_opt4 = "",
    ytdl_opt5 = "",
    ytdl_opt6 = "",
    ytdl_opt7 = "",
    ytdl_opt8 = "",
    ytdl_opt9 = "",
}
options.read_options(opts, "ytdl_preload")
local additionalOpts = {}
for k, v in pairs(opts) do
    if k:find("ytdl_opt%d") and v ~= "" then
        additionalOpts[k] = v
        -- print("entry")
        -- print(k .. v)
    end
end
local cachePath = opts.temp

local chapter_list = {}
local json = ""
local filesToDelete = {}

local function exists(file)
    local ok, err, code = os.rename(file, file)
    if not ok then
        if code == 13 then -- Permission denied, but it exists
            return true
        end
    end
    return ok, err
end
local function useNewLoadfile()
    for _, c in pairs(mp.get_property_native("command-list")) do
        if c["name"] == "loadfile" then
            for _, a in pairs(c["args"]) do
                if a["name"] == "index" then
                    return true
                end
            end
        end
    end
end
--from ytdl_hook
local function time_to_secs(time_string)
    local ret
    local a, b, c = time_string:match("(%d+):(%d%d?):(%d%d)")
    if a ~= nil then
        ret = (a * 3600 + b * 60 + c)
    else
        a, b = time_string:match("(%d%d?):(%d%d)")
        if a ~= nil then
            ret = (a * 60 + b)
        end
    end
    return ret
end
local function extract_chapters(data, video_length)
    local ret = {}
    for line in data:gmatch("[^\r\n]+") do
        local time = time_to_secs(line)
        if time and (time < video_length) then
            table.insert(ret, { time = time, title = line })
        end
    end
    table.sort(ret, function(a, b) return a.time < b.time end)
    return ret
end
local function chapters()
    if json.chapters then
        for i = 1, #json.chapters do
            local chapter = json.chapters[i]
            local title = chapter.title or ""
            if title == "" then
                title = string.format('Chapter %02d', i)
            end
            table.insert(chapter_list, { time = chapter.start_time, title = title })
        end
    elseif not (json.description == nil) and not (json.duration == nil) then
        chapter_list = extract_chapters(json.description, json.duration)
    end
end
--end ytdl_hook
local title = ""
local fVideo = ""
local fAudio = ""
local function load_files(dtitle, destination, audio, wait)
    if wait then
        if exists(destination .. ".mka") then
            print("---wait success: found mka---")
            audio = "audio-file=" .. destination .. '.mka,'
        else
            print("---could not find mka after wait, audio may be missing---")
        end
    end
    -- if audio ~= "" then
    --  table.insert(filesToDelete, destination .. ".mka")
    -- end
    -- table.insert(filesToDelete, destination .. ".mkv")
    dtitle = dtitle:gsub("-" .. ("[%w_-]"):rep(11) .. "$", "")
    dtitle = dtitle:gsub("^" .. ("%d"):rep(10) .. "%-", "")
    if useNewLoadfile() then
        mp.commandv("loadfile", destination .. ".mkv", "append", -1,
            audio .. 'force-media-title="' .. dtitle .. '",demuxer-max-back-bytes=1MiB,demuxer-max-bytes=3MiB,ytdl=no')
    else
        mp.commandv("loadfile", destination .. ".mkv", "append",
            audio .. 'force-media-title="' .. dtitle .. '",demuxer-max-back-bytes=1MiB,demuxer-max-bytes=3MiB,ytdl=no')                                                --,sub-file="..destination..".en.vtt") --in case they are not set up to autoload
    end
    mp.commandv("playlist_move", mp.get_property("playlist-count") - 1, nextIndex)
    mp.commandv("playlist_remove", nextIndex + 1)
    caught = true
    title = ""
    -- pop = true
end

local listenID = ""
local function listener(event)
    if not caught and event.prefix == mp.get_script_name() and string.find(event.text, listenID) then
        local destination = string.match(event.text, "%[download%] Destination: (.+).mkv") or
            string.match(event.text, "%[download%] (.+).mkv has already been downloaded")
        -- if destination then print("---"..cachePath) end;
        if destination and string.find(destination, string.gsub(cachePath, '~/', '')) then
            -- print(listenID)
            mp.unregister_event(listener)
            _, title = utils.split_path(destination)
            local audio = ""
            if fAudio == "" then
                load_files(title, destination, audio, false)
            else
                if exists(destination .. ".mka") then
                    audio = "audio-file=" .. destination .. '.mka,'
                    load_files(title, destination, audio, false)
                else
                    print("---expected mka but could not find it, waiting for 2 seconds---")
                    mp.add_timeout(2, function()
                        load_files(title, destination, audio, true)
                    end)
                end
            end
        end
    end
end

--from ytdl_hook
mp.add_hook("on_preloaded", 10, function()
    if string.find(mp.get_property("path"), cachePath) then
        chapters()
        if next(chapter_list) ~= nil then
            mp.set_property_native("chapter-list", chapter_list)
            chapter_list = {}
            json = ""
        end
    end
end)
--end ytdl_hook
function dump(o)
    if type(o) == 'table' then
        local s = '{ '
        for k, v in pairs(o) do
            if type(k) ~= 'number' then k = '"' .. k .. '"' end
            s = s .. '[' .. k .. '] = ' .. dump(v) .. ','
        end
        return s .. '} '
    else
        return tostring(o)
    end
end

local function addOPTS(old)
    for k, v in pairs(additionalOpts) do
        -- print(k)
        if string.find(v, "%s") then
            for l, w in string.gmatch(v, "([-%w]+) (.+)") do
                table.insert(old, l)
                table.insert(old, w)
            end
        else
            table.insert(old, v)
        end
    end
    -- print(dump(old))
    return old
end

local AudioDownloadHandle = {}
local VideoDownloadHandle = {}
local JsonDownloadHandle = {}
local function download_files(id, success, result, error)
    if result.killed_by_us then
        return
    end
    local jfile = cachePath .. "/" .. id .. ".json"

    local jfileIO = io.open(jfile, "w")
    jfileIO:write(result.stdout)
    jfileIO:close()
    json = utils.parse_json(result.stdout)
    -- print(dump(json))
    if json.requested_downloads[1].requested_formats ~= nil then
        local args = { ytdl, "--no-continue", "-q", "-f", fAudio, "--restrict-filenames", "--no-playlist", "--no-part",
            "-o", cachePath .. "/" .. id .. "-%(title)s-%(id)s.mka", "--load-info-json", jfile }
        args = addOPTS(args)
        AudioDownloadHandle = mp.command_native_async({
            name = "subprocess",
            args = args,
            playback_only = false
        }, function()
        end)
    else
        fAudio = ""
        fVideo = fVideo:gsub("bestvideo", "best")
        fVideo = fVideo:gsub("bv", "best")
    end

    local args = { ytdl, "--no-continue", "-f", fVideo .. '/best', "--restrict-filenames", "--no-playlist",
        "--no-part", "-o", cachePath .. "/" .. id .. "-%(title)s-%(id)s.mkv", "--load-info-json", jfile }
    args = addOPTS(args)
    VideoDownloadHandle = mp.command_native_async({
        name = "subprocess",
        args = args,
        playback_only = false
    }, function()
    end)
end

local function DL()
    local index = tonumber(mp.get_property("playlist-pos"))
    if mp.get_property("playlist/" .. index .. "/filename"):find("/videos$") and mp.get_property("playlist/" .. index + 1 .. "/filename"):find("/shorts$") then
        return
    end
    if tonumber(mp.get_property("playlist-pos-1")) > 0 and mp.get_property("playlist-pos-1") ~= mp.get_property("playlist-count") then
        nextIndex = index + 1
        local nextFile = mp.get_property("playlist/" .. nextIndex .. "/filename")
        if nextFile and caught and nextFile:find("://", 0, false) then
            caught = false
            mp.enable_messages("info")
            mp.register_event("log-message", listener)
            local ytFormat = mp.get_property("ytdl-format")
            fVideo = string.match(ytFormat, '(.+)%+.+//?') or 'bestvideo'
            fAudio = string.match(ytFormat, '.+%+(.+)//?') or 'bestaudio'
            -- print("start"..nextFile)
            listenID = tostring(os.time())
            local args = { ytdl, "--dump-single-json", "--no-simulate", "--skip-download",
                "--restrict-filenames",
                "--no-playlist", "--sub-lang", "en", "--write-sub", "--no-part", "-o",
                cachePath .. "/" .. listenID .. "-%(title)s-%(id)s.%(ext)s", nextFile }
            args = addOPTS(args)
            -- print(dump(args))
            table.insert(filesToDelete, listenID)
            JsonDownloadHandle = mp.command_native_async({
                name = "subprocess",
                args = args,
                capture_stdout = true,
                capture_stderr = true,
                playback_only = false
            }, function(...)
                download_files(listenID, ...)
            end)
        end
    end
end

local function clearCache()
    -- print(pop)

    --if pop == true then
    mp.abort_async_command(AudioDownloadHandle)
    mp.abort_async_command(VideoDownloadHandle)
    mp.abort_async_command(JsonDownloadHandle)
    -- for k, v in pairs(filesToDelete) do
    --  print("remove: " .. v)
    --  os.remove(v)
    -- end
    local ftd = io.open(cachePath .. "/temp.files", "a")
    for k, v in pairs(filesToDelete) do
        ftd:write(v .. "\n")
        if package.config:sub(1, 1) ~= '/' then
            os.execute('del /Q /F "' .. cachePath .. "\\" .. v .. '*"')
        else
            os.execute('rm -f ' .. cachePath .. "/" .. v .. "*")
        end
    end
    ftd:close()
    print('clear')
    mp.command("quit")
    --end
end
mp.add_hook("on_unload", 50, function()
    -- mp.abort_async_command(AudioDownloadHandle)
    -- mp.abort_async_command(VideoDownloadHandle)
    mp.abort_async_command(JsonDownloadHandle)
    mp.unregister_event(listener)
    caught = true
    listenID = "resetYtdlPreloadListener"
    -- print(listenID)
end)

local skipInitial
mp.observe_property("playlist-count", "number", function()
    if skipInitial then
        DL()
    else
        skipInitial = true
    end
end)

--from ytdl_hook
local platform_is_windows = (package.config:sub(1, 1) == "\\")
local o = {
    exclude = "",
    try_ytdl_first = false,
    use_manifests = false,
    all_formats = false,
    force_all_formats = true,
    ytdl_path = "",
}
local paths_to_search = { "yt-dlp", "yt-dlp_x86", "youtube-dl" }
--local options = require 'mp.options'
options.read_options(o, "ytdl_hook")

local separator = platform_is_windows and ";" or ":"
if o.ytdl_path:match("[^" .. separator .. "]") then
    paths_to_search = {}
    for path in o.ytdl_path:gmatch("[^" .. separator .. "]+") do
        table.insert(paths_to_search, path)
    end
end

local function exec(args)
    local ret = mp.command_native({
        name = "subprocess",
        args = args,
        capture_stdout = true,
        capture_stderr = true
    })
    return ret.status, ret.stdout, ret, ret.killed_by_us
end

local msg = require 'mp.msg'
local command = {}
for _, path in pairs(paths_to_search) do
    -- search for youtube-dl in mpv's config dir
    local exesuf = platform_is_windows and ".exe" or ""
    local ytdl_cmd = mp.find_config_file(path .. exesuf)
    if ytdl_cmd then
        msg.verbose("Found youtube-dl at: " .. ytdl_cmd)
        ytdl = ytdl_cmd
        break
    else
        msg.verbose("No youtube-dl found with path " .. path .. exesuf .. " in config directories")
        --search in PATH
        command[1] = path
        es, json, result, aborted = exec(command)
        if result.error_string == "init" then
            msg.verbose("youtube-dl with path " .. path .. exesuf .. " not found in PATH or not enough permissions")
        else
            msg.verbose("Found youtube-dl with path " .. path .. exesuf .. " in PATH")
            ytdl = path
            break
        end
    end
end
--end ytdl_hook

mp.register_event("start-file", DL)
mp.register_event("shutdown", clearCache)
local ftd = io.open(cachePath .. "/temp.files", "r")
while ftd ~= nil do
    local line = ftd:read()
    if line == nil or line == "" then
        ftd:close()
        io.open(cachePath .. "/temp.files", "w"):close()
        break
    end
    -- print("DEL::"..line)
    if package.config:sub(1, 1) ~= '/' then
        os.execute('del /Q /F "' .. cachePath .. "\\" .. line .. '*" >nul 2>nul')
    else
        os.execute('rm -f ' .. cachePath .. "/" .. line .. "* &> /dev/null")
    end
end

it will now download the first video when you start playing the last one

it will now download the first video when you start playing the last one

What happens if I only paste one Youtube link to MPV? Does it download video immediately or after playing the first time?

no, that's a bit out of the scope of "preloading" in my opinion. Personally, I do have a chain of scripts that does that for me but it does also add considerable startup time for the video, like triple or more.