TestWatcherRecoversAfterCompaction is flaky

## Flaky Test
### Which jobs are failing
```text
[INFO] [index.go:214] ["compact tree index"] [revision=25]
[INFO] [kvstore_compaction.go:69] ["finished scheduled compaction"] [compact-revision=25] [took=2.269587ms] [hash=808340559] [current-db-size-bytes=77824] [current-db-size="78 kB"] [current-db-size-in-use-bytes=77824] [current-db-size-in-use="78 kB"]
[INFO] [hash.go:137] ["storing new hash"] [hash=808340559] [revision=25] [compact-revision=-1]
testutil.go:68:
Error Trace: /home/prow/go/src/github.com/tikv/pd/pkg/utils/testutil/testutil.go:68
Error: Condition never satisfied
Test: TestResourceManagerWatcherMatrix/TestWatcherRecoversAfterCompaction
```
### CI link
- https://prow.tidb.net/view/gs/prow-tidb-logs/pr-logs/pull/tikv_pd/10498/pull-unit-test-next-gen-3/2045051261622947840
- https://github.com/tikv/pd/actions/runs/24559889901/job/71805626479
### Reason for failure (if possible)

### Anything else
package=tests/integrations/mcs/resourcemanager;
test=TestWatcherRecoversAfterCompaction
failure_item_ids=[prow:prow-pull-unit-test-next-gen-3-2045051261622947840:TestWatcherRecoversAfterCompaction,actions:actions-24559889901-71805626479:TestWatcherRecoversAfterCompaction]

Start by running TestResourceManagerWatcherMatrix/TestWatcherRecoversAfterCompaction in tests/integrations/mcs/resourcemanager and review the linked CI logs around compaction and recovery. Trace the condition reported at testutil.go:68 to identify why the watcher does not recover reliably. Done means the test passes repeatedly and no longer flakes in CI.

Written by the indexing model from the issue text.