WP Trac #42573: Fix for theme template caching. https://core.trac.wordpress.org/ticket/42573

wp-42573.php

<?php
/**
 * Plugin name: WP Trac #42573: Fix for theme template file caching.
 * Description: Flush the theme file cache each time the admin screens are loaded which uses the file list.
 * Plugin URI: https://core.trac.wordpress.org/ticket/42573
 * Author: Weston Ruter, XWP.
 * Author URI: https://weston.ruter.net
 */

function wp_42573_fix_template_caching( WP_Screen $current_screen ) {

	// Only flush the file cache with each request to post list table, edit post screen, or theme editor.
	if ( ! in_array( $current_screen->base, array( 'post', 'edit', 'theme-editor' ), true ) ) {
		return;
	}

	$theme = wp_get_theme();
	if ( ! $theme ) {
		return;
	}

	$cache_hash = md5( $theme->get_theme_root() . '/' . $theme->get_stylesheet() );
	$label = sanitize_key( 'files_' . $cache_hash . '-' . $theme->get( 'Version' ) );
	$transient_key = substr( $label, 0, 29 ) . md5( $label );
	delete_transient( $transient_key );
}
add_action( 'current_screen', 'wp_42573_fix_template_caching' );

Sorry, I can't. Please reach out to the support forums: https://wordpress.org/support/

As @westonruter mentioned, it is now part of WordPress core. However, my new page template was still not showing up after adding it to the folder.

For me, I had two differently named page templates, but the Template Name between both was the same.

You can find this in the top level php tag. I updated the template name to something different and it immediately populated in my dropdown.

Source: https://vanseodesign.com/wordpress/wp-page-templates-dropdown/