See https://wordpress.org/support/topic/amp-jetpack-subscribe-button-stopped-working/

jetpack-subscriptions-widget-amp-workaround.php

<?php
/**
 * Plugin Name: Jetpack Subscriptions Widget AMP Workaround (and Ajax Enhancements)
 * Description: Fix issue with form submission in AMP not including the name of clicked submit button. Also make use of Ajax to show the success/failure of the submission.
 * Plugin URI: https://wordpress.org/support/topic/amp-jetpack-subscribe-button-stopped-working/
 * Author Name: Weston Ruter
 * Author URI: https://weston.ruter.net/
 * Version: 1.0
 * License: GPLv2 or later
 */

/*
 * Ensure that \Jetpack_Subscriptions::widget_submit() will run at the template_redirect action.
 * See https://github.com/Automattic/jetpack/blob/e3986c699471dbb1dab42bdeac2041b8c979514c/modules/subscriptions.php#L84
 */
if ( isset( $_SERVER['REQUEST_METHOD'] ) && 'POST' === $_SERVER['REQUEST_METHOD'] && isset( $_REQUEST['action'] ) && 'subscribe' === $_REQUEST['action'] ) {
	$_REQUEST['jetpack_subscriptions_widget'] = true;
}

// -----------THE REST OF THIS PLUGIN IS OPTIONAL------------------

/*
 * The following code is used to implement Ajax-based submission of the subscription form.
 * Instead of the page reloading to display the success/failure of the subscription, the
 * success/error response will be displayed at the top of the form.
 * This should really be factored into the Jetpack plugin generally.
 */

add_action(
	'jetpack_subscriptions_form_submission',
	/**
	 * Intercept the redirect after the subscription form submission request to instead return with JSON response.
	 *
	 * Most of the code in this function comes from Jetpack_Subscriptions_Widget::render_widget_status_messages().
	 *
	 * @see \Jetpack_Subscriptions_Widget::render_widget_status_messages()
	 * @param string $result Result code.
	 */
	function( $result ) {
		if ( ! function_exists( 'get_jetpack_blog_subscriptions_widget_classname' ) ) {
			return;
		}

		global $wp_widget_factory;
		if ( ! isset( $wp_widget_factory->widgets[ get_jetpack_blog_subscriptions_widget_classname() ] ) ) {
			return;
		}

		// Determine the success message for the widget.
		$success_message = '';

		/**
		 * Subscriptions widget instance (object).
		 *
		 * @var Jetpack_Subscriptions_Widget $widget_object
		 */
		$widget_object = $wp_widget_factory->widgets[ get_jetpack_blog_subscriptions_widget_classname() ];

		$widget_number = 0;
		if ( isset( $_REQUEST['redirect_fragment'] ) ) {
			$widget_number = intval( preg_replace( '/^.+?-(?=\d+$)/', '', $_REQUEST['redirect_fragment'] ) );
		}

		if ( $widget_number ) {
			$instances = $widget_object->get_settings();
			if ( isset( $instances[ $widget_number ]['success_message'] ) ) {
				$success_message = $instances[ $widget_number ]['success_message'];
			}
		}

		$error   = null;
		$success = null;

		switch ( $result ) {
			case 'invalid_email' :
				$error = sprintf( '<p class="error">%s</p>', esc_html__( 'The email you entered was invalid. Please check and try again.', 'jetpack' ) );
				break;
			case 'opted_out' :
				$error = sprintf(
					'<p class="error">%s</p>',
					sprintf(
						__( 'The email address has opted out of subscription emails. <br /> You can manage your preferences at <a href="%1$s" title="%2$s" target="_blank">subscribe.wordpress.com</a>', 'jetpack' ),
						'https://subscribe.wordpress.com/',
						__( 'Manage your email preferences.', 'jetpack' )
					)
				);
				break;
			case 'already' :
				$error = sprintf(
					'<p class="error">%s</p>',
					sprintf(
						__( 'You have already subscribed to this site. Please check your inbox. <br /> You can manage your preferences at <a href="%1$s" title="%2$s" target="_blank">subscribe.wordpress.com</a>', 'jetpack' ),
						'https://subscribe.wordpress.com/',
						__( 'Manage your email preferences.', 'jetpack' )
					)
				);
				break;
			case 'success' :
				$success = sprintf( '<p class="success">%s</p>', wpautop( str_replace( '[total-subscribers]', number_format_i18n( $widget_object::fetch_subscriber_count()['value'] ), $success_message ) ) );
				break;
			default :
				$error = sprintf( '<p class="error">%s</p>', esc_html__( 'There was an error when subscribing. Please try again.', 'jetpack' ) );
				break;
		}

		wp_send_json( compact( 'success', 'error' ), $success ? 200 : 400 );
	},
	PHP_INT_MAX
);

// Add sanitizer for injecting the success/error response containers to the subscription form.
add_filter(
	'amp_content_sanitizers',
	function ( $sanitizers ) {
		class AMP_Jetpack_Subscriptions_Form_Response_Container_Injector extends AMP_Base_Sanitizer {
			function sanitize() {
				$xpath = new DOMXPath( $this->dom );
				/**
				 * @var DOMElement $form
				 */
				foreach ( $xpath->query( '//form[ starts-with( @id, "subscribe-blog-blog_subscription" ) ]' ) as $form ) {
					$form->insertBefore( $this->create_message_container( 'error' ), $form->firstChild );
					$form->insertBefore( $this->create_message_container( 'success' ), $form->firstChild );
				}
			}

			function create_message_container( $type ) {
				$div      = $this->dom->createElement( 'div' );
				$template = $this->dom->createElement( 'template' );
				$mustache = $this->dom->createTextNode( '{{{' . $type . '}}}' );
				$div->setAttribute( 'submit-' . $type, '' );
				$template->setAttribute( 'type', 'amp-mustache' );
				$template->appendChild( $mustache );
				$div->appendChild( $template );
				return $div;
			}
		}

		$sanitizers = array_merge(
			array(
				'AMP_Jetpack_Subscriptions_Form_Response_Container_Injector' => array(),
			),
			$sanitizers
		);

		return $sanitizers;
	}
);