Do not validate on post-save, only on publish

This is a continuation of issue #891 on Github, and addressed in pull-request #1378 with the last comment by Tran that

the code targets to all forms, which is quite dangerous. Please also note that it must runs in various situations: classic editor, block editor, front end forms, user profile, etc.

I am going to re-add this functionality manually, but would like to officially open a support request to determine the best way to add a hook or filter so the core does not need to be modified.