Use lockfile-based approach for precaching manifest for tests

[bhollis]

In #10068 I said:

An alternative I was thinking about was to use a lockfile strategy, leveraging node-proper-lockfile - this has the advantage of not requiring the pre-cache step but would still require most of the other machinery (deleting all but the most recent file for GHA caching, using the most recent file to avoid calling the manifest API a ton, etc) and the logic will be pretty complicated. I might try it out after this, but for now, this should resolve our test flakiness issues.

This is a good idea, even though it's complicated. The current solution really slows down running tests in VSCode.

[bhollis]

An alternative, which may be simpler, is to store everything in a SQLite database, which natively supports multi-process concurrency via transactions.