The PostVisibility is an ancient component (in React years) and needs some refreshing. Props @afercia for giving me this idea (#69440).

This is a two-part issue combined in one.

1. Replace custom fieldset and PostVisibilityChoice with RadioControl.
2. Remove the confirmation step and immediate post publishing when selecting "Private" status. This doesn't match the logic in the document settings and is confusing.

I did some archeology regarding the second part, and it seems the "Confirm and Publish" step was introduced to prevent autosaves from accidentally publishing a post (ref #945 (comment)). Fortunately for us, this was resolved in #62171.