Add relay_lock to cache-handling, formatting #1957

Job	Run time
Prepare	51s
Shellcheck	6s
Dependency	4s
Ruff check and force	6s
Check commit	46s
Create pytest cache for Python 3.13	6s
Run pytest using Python 3.13	21s
Run mypy	7s
Process test coverage	13s
Process test complexity	10s
Build and publish Python 🐍 distributions 📦 to TestPyPI	21s
	3m 11s

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