feat(playwright): add durable settings browser test suite - #5773

Bugbot Analysis Progress (5m 38s elapsed)

✅ Gathered PR context (7s)
✅ Completed bug detection (5m 30s)
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Final Result: Bugbot completed review - no issues found! ✅

Request ID: serverGenReqId_e0e3b089-8a8d-4a21-8fdc-9a455288d119