Preserve tap checkout authentication

[0x77dev]

Copies actions/checkout's repository-local App authentication header into the moved canonical Homebrew tap checkout before pushing the Formula branch.\n\nVerified: actionlint .github/workflows/ci.yml; git diff --check.

[greptile-apps]

Confidence Score: 5/5

Safe to merge based on the exercised relocation behavior: authentication is required before moving the checkout and remains available afterward.

The changed shell behavior was executed in isolated local Git repositories for both the missing-header failure path and the valid-header success path, with the expected filesystem and configuration results observed.

Files Needing Attention: No files need additional attention; .github/workflows/ci.yml was covered by the relocation checks.

T-Rex Logs

What T-Rex did

• Ran the reviewed relocation commands in disposable local Git repositories with no network access or real credentials.
• When the authentication header was absent, the updated relocation exited with status 1 before creating either the canonical checkout or the compatibility symlink.
• With a fake valid AUTHORIZATION header, the relocation moved the checkout and both the canonical path and the original symlink resolved the same header.
• In a follow-up validation pass, a missing header caused relocation to exit 1 with no canonical checkout or symlink, while a valid header allowed canonical checkout and the original symlink to resolve to the same header.

_{Ran code and verified through T-Rex}

_{Reviews (1): Last reviewed commit: "Preserve tap checkout authentication" | Re-trigger Greptile}