Refactoring: Introduce `overlay/caching.ts` #9684

Job	Run time
Split workflow (macos-latest, linked)	1m 23s
Split workflow (ubuntu-latest, default)	1m 9s
Split workflow (ubuntu-latest, linked)	1m 12s
Split workflow (ubuntu-latest, nightly-latest)	1m 20s
Split workflow (macos-latest, default)	1m 45s
Split workflow (macos-latest, nightly-latest)	1m 31s
	8m 20s

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