fix(server): memoise git top-level lookup in repository identity resolver

[leorivastech]

What Changed

RepositoryIdentityResolver.resolve ran git rev-parse --show-toplevel on every call. That top-level lookup sat outside the existing identity cache, so it spawned a git subprocess every time, even for the same workspace. This memoises the cwd to top-level mapping in its own cache keyed by cwd, so repeated resolves reuse the result.

Only a resolved top-level is cached (positive TTL). A failed or timed-out lookup is not cached, so the next resolve retries rev-parse and recovers the real root instead of pinning the identity rootPath to a nested path; this keeps the pre-change behaviour for the failure path. Behaviour is otherwise unchanged.

Why

This is the Fix 1 quick win from #2037. replayEvents enriches every project.* event on each reconnect, and that enrichment calls RepositoryIdentityResolver.resolve once per project. With the top-level lookup uncached, a replay burst spawned one git process per project event every time, which is a big part of what pushed replayEvents past the 15s SLOW_RPC_ACK_THRESHOLD_MS and triggered the persistent "Some requests are slow" toast.

#2083 already landed Fix 2 (the negative cache TTL) from the same issue; this takes the next small, self-contained slice. It does not close #2037, which still tracks the remaining proposed fixes.

Regression tests use a counting ProcessRunner: resolving the same workspace twice runs git rev-parse --show-toplevel once instead of twice, and a transient first-call timeout still retries on the next resolve and reports the top-level root.

Checklist

• This PR is small and focused
• I explained what changed and why
• I included before/after screenshots for any UI changes
• I included a video for animation/interaction changes

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[cursor]

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Approvability

Verdict: Approved

Performance optimization that adds memoization for git subprocess lookups to reduce repeated calls during replay events. Changes are self-contained, well-tested, and don't modify user-facing behavior beyond performance improvement.

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[leorivastech]

Pushed a follow-up commit (a911c15) that addresses the Cursor Bugbot comment above.

Failed or timed-out git rev-parse --show-toplevel lookups are no longer cached. Only a resolved top-level gets the positive TTL; otherwise the next resolve re-runs rev-parse and recovers the real root, which keeps the behaviour from before this PR. I also added a regression test that times out the first lookup and asserts the second resolve retries and reports the top-level rootPath instead of the nested path.