Investigate the 50min test case br_serv_outage

[3pointer]

Please answer these questions before submitting your issue. Thanks!

1. What did you do?
   If possible, provide a recipe for reproducing the error.
   In release-4.0 , we found a case costs nearly 50mins. https://ci.pingcap.net/blue/organizations/jenkins/br_ghpr_unit_and_integration_test/detail/br_ghpr_unit_and_integration_test/5483/pipeline/87/

2. What did you expect to see?
   a stable lower cost in integration tests.

3. What did you see instead?
   The case costs 50mins.

4. What version of BR and TiDB/TiKV/PD are you using?

5. Operation logs

   • Please upload br.log for BR if possible
   • Please upload tidb-lightning.log for TiDB-Lightning if possible
   • Please upload tikv-importer.log from TiKV-Importer if possible
   • Other interesting logs

6. Configuration of the cluster and the task

   • tidb-lightning.toml for TiDB-Lightning if possible
   • tikv-importer.toml for TiKV-Importer if possible
   • topology.yml if deployed by TiUP

7. Screenshot/exported-PDF of Grafana dashboard or metrics' graph in Prometheus if possible