The 5h limit is gone (for now). It does not presently need to be chased. :)

For the automated checking of other stuff: It was a one-shot prompt to get Codex clank up some Python that returns remaining usage, next reset time/date, and so on.

The result does use Codex App Server, but it's a short-lived process that is dealt with over stdio so that's... fine-ish, I guess?