Wordpress: Auto set page template for child pages to be the same as parent.

wp-set-child-page-template.php

<?php
/**
 * Wordpress: Auto set page template for child pages to be the same as parent.
 */
function set_child_page_template( $post_id, $post, $update ) {
	// Check for post type page
	if( $post->post_type === 'page' ) {
		// Check if its a child page
		if( $post->post_parent !== 0 ) {
			// If its child get the post parent template
			$parent_template = get_post_meta( $post->post_parent, '_wp_page_template', true );
			update_post_meta( $post_id, '_wp_page_template', $parent_template );
		} else {
			// If its parent update all his childs
			$parent_template = get_post_meta( $post_id, '_wp_page_template', true );
			$children = get_pages( ['child_of'=>$post_id] );
			foreach( $children as $child ) {
				update_post_meta( $child->ID, '_wp_page_template', $parent_template );
			}
		}
	}

}
add_action('save_post', 'set_child_page_template', 10, 3);