Switch template based on page parent or grandparent. Requires the page parent template is set.

parent_template_switch.php

// Switch template based on page parent or grandparent. Requires the page parent template is set.
add_action('template_include', 'auto_child_template');

function auto_child_template( $template = '' ) {
    global $post;
    
        if ( ! is_page() ) {
            return $template;
        } 
        else {
            $page = get_queried_object();
            $ancestors = get_post_ancestors( $post );
            $templates = array();
            // add ancestors page templates to $templates array
            foreach ( $ancestors as $ancestor ) {
              $templates[] = get_page_template_slug( $ancestor );
            }
            // remove empty values
            $templates = array_filter($templates);
            // if no ancestors has a template return current one
            if ( empty($templates) ) return $template;
            // fallback
            $templates[] = 'page.php';
            return locate_template( $templates, FALSE );
        }
}