Convert from using GitHub App ID to GitHub Client ID

### TL;DR

GitHub made the two interchangeable but hints that future features will only work with the client id. At some point we'll want to get ahead of that change.
https://github.blog/changelog/2024-05-01-github-apps-can-now-use-the-client-id-to-fetch-installation-tokens/

This is a low priority issue, adding it here so we don't forget about it.

### Detailed design

_No response_

### Alternatives considered

_No response_

### Additional information

_No response_