Fixes #8313 by calling the GitHub API to determine how much the CTS clone needs to be deepened to obtain the desired revision.

This seems like it will not be exercised very often, and could bit rot before it ever gets used. Feel free to say "just because you can, doesn't mean you should" and decline this PR.

Putting the branch name in all of our GitHub actions cache keys seems like a reasonable thing to do for various reasons, and would prevent this issue happening again in CI, but this fix is more general because it also handles developer checkouts and a revert of a CTS version bump.

Testing
Tested manually.

Squash or Rebase? Squash

Checklist

• Run cargo fmt.
• Run taplo format.
• Run cargo clippy --tests. If applicable, add:
  • --target wasm32-unknown-unknown
• Run cargo xtask test to run tests.
• If this contains user-facing changes, add a CHANGELOG.md entry.