Feature Request: Enable GitHub authentication through GitHub Apps

First of all, this tool is amazing!

## What
Integrate [authentication with GitHub Apps](https://docs.github.com/en/developers/apps/building-github-apps/authenticating-with-github-apps#authenticating-as-a-github-app), because it is more granular with the permissions than a PAT.
Also, PAT requires a user for this (which consumes a license), a GitHub App does not.

## Why
GitHub App has more **granular permissions** than the PAT, and allows for repo-whitelisting, which can be be very helpful.
Also, as stated above, a PAT requires a user for this (which consumes a license), where GitHub App does not.

Start by reading the linked GitHub documentation on authenticating with GitHub Apps and inspect the repository entry points for its current PAT-based authentication. Define how GitHub App credentials, granular permissions, and repository allowlisting should be represented. Done means the tool can authenticate through a GitHub App without requiring a PAT-backed user.

Written by the indexing model from the issue text.