How to use the post_title of custom post type as taxonomy

Question

I have a few custom post types to define various types of content and one CPT to configure which fields should get rendered. The config CPT also defines a taxonomy so I can pick and choose with which config a CPT gets rendered.
The taxonomy term is defined by the post_title of its CPT.

Adding a term to the taxonomy is no problem hooking into the save_post-hook.
My problem is with changing the name of a taxonomy or deleting it. The expected behaviour is that when I change the post_title of my taxonomy that the name of the exixtig taxonomy term gets also changed. At this time there is just a new one added.
Same with deleting the CP which defines a taxonomy.

Is there a hook that actually only fires when a post gets updated and where I can get $post_before and $post_after?
If not, how can I reliably check if a post gets updated?
The save_post-hook gets fired when creating a post for the first time as well as when updating an existing post which is a bit annoying.

Answer 1

Is there a hook that actually only fires when a post gets updated and where I can get $post_before and $post_after?

You're probably looking for the post_updated hook.

Usage

add_action( 'post_updated', 'wpse_264720_post_updated', 10, 3 );
function wpse_264720_post_updated( $post_ID, $post_after, $post_before ) {

  //* Bail if this is an autosave
  if( defined( 'DOING_AUTOSAVE' ) && DOING_AUTOSAVE ) {
    return;
  }

  //* Bail if this is a post revision
  if( wp_is_post_revision( $post_ID ) ) {
    return;
  }

  //* Bail if not the correct post types
  if( ! in_array( $post_after->post_type, [ 'post-type-1', 'post-type-2' ] ) ) {
    return;
  }

  //* If you add/update/delete posts, remove action to avoid infinite loop
  remove_action( 'post_updated', 'wpse_264720_post_updated', 10 );

  //* Do something useful after the post was updated

  //* If the post was updated, remove save_post action
  remove_action( 'save_post', 'wpse_264720_save_post', 10, 3 );
}
//* Hypothetical function hooked to save_post
add_action( 'save_post', 'wpse_264720_save_post', 10, 3 );
function wpse_264720_save_post( $post_id, $post, $update ) {
  //* Bail if post was an update
  if( $update ) {
    return;
  }
  //* Do something useful on save_post
}