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

action.yml

@@ -5,7 +5,9 @@ runs:
   main: "dist/index.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 }}
   publish-script:
@@ -38,14 +40,13 @@ inputs:
       this option will also always be `true`.
     required: false
     default: true
-  commit-mode:
+  push-with-git-cli:
     description: >
-      An enum to specify the commit mode. Use "git-cli" to push changes using the Git CLI,
-      or "github-api" to push changes via the GitHub API. When using "github-api",
-      all commits and tags are signed using GitHub's GPG key and attributed to the user
-      or app who owns the GITHUB_TOKEN.
+      Whether to use the Git CLI instead of the GitHub API to push release commits and tags.
+      Defaults to `false`. When using the GitHub API, commits and tags are signed using
+      GitHub's GPG key and attributed to the user or app that owns the `github-token`.
     required: false
-    default: "git-cli"
+    default: false
 outputs:
   published:
     description: A "true" or "false" string value to indicate whether a publishing is happened or not