fix: use GitHub App token for Batteries/Mathlib checkout in PR release

The MATHLIB4_BOT PAT has been deprecated as part of the migration to GitHub Apps.
This PR updates the workflow to use the mathlib-nightly-testing GitHub App instead.

**Required setup:** Add the following secrets to leanprover/lean4:
- MATHLIB_NIGHTLY_TESTING_APP_ID
- MATHLIB_NIGHTLY_TESTING_PRIVATE_KEY

These are the same values used in leanprover-community/mathlib4 and batteries.