How to Programmatically Trigger the Update of a Post in WordPress?

The function as written there will succeed silently, since you haven’t actually passed in any data to change. You should be able to see what I mean by altering your function slightly:

function trigger_post_update( $post_id ) {
   
    return wp_update_post( array( 'ID' => $post_id ), true );

}

You don’t need the get_post() to check if it exists, wp_update_post() will do that for you and return a WP_Error if it doesn’t (without the second parameter it will just return 0). On success the function will return the ID you passed in.