dr-autosync: move state replicate to different goroutine (#6874)

[ti-chi-bot]

This is an automated cherry-pick of #6874

What problem does this PR solve?

Issue Number:

What is changed and how does it work?

when backup cluster is disconnected, because that PD cannot replicate state to PD that is in backup cluster, the state change is too slow (because it needs to wait I/O timeout)

move state change to different goroutine.

Check List

Tests

• Unit test

Related changes

• PR to update pingcap/docs/pingcap/docs-cn:
• PR to update pingcap/tiup:
• Need to cherry-pick to the release branch: release-6.5

Release note

None.

[ti-chi-bot]

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[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	5cc7fae	link	true	/test build

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