server: advance ServerStart check (#8951)

[ti-chi-bot]

This is an automated cherry-pick of #8951

What problem does this PR solve?

Issue Number: Close #8950

What is changed and how does it work?

Check List

Tests

• Unit test
• Integration test
• Manual test (add detailed scripts or steps below)
• No code

Release note

Fix the problem that PD may panic after enable `tidb_enable_tso_follower_proxy`.

[ti-chi-bot]

@ti-chi-bot: The following test failed, say /retest to rerun all failed tests or /retest-required to rerun all mandatory failed tests:

Test name	Commit	Details	Required	Rerun command
idc-jenkins-ci/build	66967bc	link	true	/test build

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[ti-chi-bot]

[APPROVALNOTIFIER] This PR is APPROVED

This pull-request has been approved by: lhy1024, okJiang

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[ti-chi-bot]

[LGTM Timeline notifier]

Timeline:

• 2025-01-03 08:47:45.716502372 +0000 UTC m=+685801.072506930: ☑️ agreed by okJiang.
• 2025-01-06 03:23:46.932849374 +0000 UTC m=+151170.221681078: ☑️ agreed by lhy1024.

[okJiang]

/retest