* perf(app): skip transient replica cache writes
The replica cache subscribed to the entire session store, so live stream-head updates forced repeated JSON serialization and browser storage writes even though the head is not persisted. Select the cache's persisted inputs once and schedule writes only when that projection changes.
* test(app): move perf cleanup into fixture
Keep the replica-cache performance scenario as a direct setup, stream, measure, and assert flow while the spec-local Playwright fixture owns deterministic mock-agent cleanup.
