chore: simplify ruby release token usage

[marandaneto]

💡 Motivation and Context

The Ruby release workflow was requesting a GitHub App token twice, once in version-bump and again in publish. Other SDK repos like posthog-react-native-session-replay only need the app token in the version-bump job, so the duplicate setup adds unnecessary complexity and another failure point.

This PR also fixes the next release failure mode: once the version bump updates lib/posthog/version.rb, Bundler sees the path gem version change and requires Gemfile.lock to be refreshed before the publish job can run with frozen lockfile settings.

This PR includes a patch changeset so merging it can exercise the release automation again.

💚 How did you test it?

• compared the Ruby workflow with posthog-react-native-session-replay/.github/workflows/release.yml
• updated publish to use the default checkout/token flow and kept the GitHub App token only in version-bump
• parsed .github/workflows/release.yml with Ruby YAML to confirm the workflow file is still valid
• added a patch changeset and verified pnpm changeset status computes the next release as 3.6.3
• locally changed the gem version and verified bundle lock updates Gemfile.lock to match, which addresses the frozen lockfile failure in publish

📝 Checklist

• I reviewed the submitted code.
• I added tests to verify the changes.
• I updated the docs if needed.
• No breaking change or entry added to the changelog.

If releasing new changes

• Ran pnpm changeset to generate a changeset file
• Added the release label to the PR