CI: Remove waiting logic in release workflow

[awaelchli]

What does this PR do?

So far, the release process had a mechanism to wait for a builds/version branch to appear while waiting on the merging of an internal repo. But this was a deadlock for a long time, and now that this internal repo no longer depends on the lightning package, we should remove the waiting logic from the package release workflow.

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📚 Documentation preview 📚: https://pytorch-lightning--20050.org.readthedocs.build/en/20050/

[github-actions]

⚡ Required checks status: All passing 🟢

Groups summary

🟢 mypy

Check ID	Status
mypy	success	✅

These checks are required after the changes to requirements/store/test.txt.

🟢 install

Check ID	Status
install-pkg (ubuntu-22.04, fabric, 3.8)	success	✅
install-pkg (ubuntu-22.04, fabric, 3.11)	success	✅
install-pkg (ubuntu-22.04, pytorch, 3.8)	success	✅
install-pkg (ubuntu-22.04, pytorch, 3.11)	success	✅
install-pkg (ubuntu-22.04, lightning, 3.8)	success	✅
install-pkg (ubuntu-22.04, lightning, 3.11)	success	✅
install-pkg (ubuntu-22.04, notset, 3.8)	success	✅
install-pkg (ubuntu-22.04, notset, 3.11)	success	✅
install-pkg (macOS-12, fabric, 3.8)	success	✅
install-pkg (macOS-12, fabric, 3.11)	success	✅
install-pkg (macOS-12, pytorch, 3.8)	success	✅
install-pkg (macOS-12, pytorch, 3.11)	success	✅
install-pkg (macOS-12, lightning, 3.8)	success	✅
install-pkg (macOS-12, lightning, 3.11)	success	✅
install-pkg (macOS-12, notset, 3.8)	success	✅
install-pkg (macOS-12, notset, 3.11)	success	✅
install-pkg (windows-2022, fabric, 3.8)	success	✅
install-pkg (windows-2022, fabric, 3.11)	success	✅
install-pkg (windows-2022, pytorch, 3.8)	success	✅
install-pkg (windows-2022, pytorch, 3.11)	success	✅
install-pkg (windows-2022, lightning, 3.8)	success	✅
install-pkg (windows-2022, lightning, 3.11)	success	✅
install-pkg (windows-2022, notset, 3.8)	success	✅
install-pkg (windows-2022, notset, 3.11)	success	✅

These checks are required after the changes to requirements/store/test.txt.

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Thank you for your contribution! 💜

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