Use GitHub API for pushes by default and require explicit github-token when using custom tokens (#692)

* Ensure `github-token` wins for `git-cli` pushes

* more shenanigans

* Default to GitHub API commit mode

* e2e auth tests

* push missing utils

* rename input

* refactor

* refactor

* refactor

* refactor

* refactor

* refactor

* reuse helpers

* refactor

* refactor

* simplify

* add tests

* refactor

* improve comments

* shift helper

* add comments

* extract test helpers

* update docs and changesets

* update one thing

pr-comment/action.yml

@@ -5,7 +5,9 @@ runs:
   main: ../dist/pr-comment.js
 inputs:
   github-token:
-    description: "The GitHub token to use for authentication. Defaults to the GitHub-provided token."
+    description: >
+      The GitHub token to use for authentication. Defaults to the GitHub-provided token.
+      To use a custom token, pass it explicitly to this input.
     required: false
     default: ${{ github.token }}
   body: