test: add integration test calling real performSync with mocked browser APIs

Add __test__ exports (VITEST-only, tree-shaken in production) to
background/index.js so integration tests can import and call the real
performSync, addTombstone, categorizeCloudBookmarks, etc.

New test file: toolbar-delete-race-integration.test.js (10 tests)
- Calls the REAL performSync with fully mocked browser.* and fetch APIs
- Simulates the tombstone race condition: delays cloud GET, fires
  onRemoved mid-sync, verifies tombstone is preserved after sync
- Verifies deleted bookmark is NOT re-added from cloud
- Tests tombstone merge, categorization filtering, concurrent sync
  guard, and state management
- All 10 tests pass; 527 total passing (was 517)

Author: Preshy