fix(runaway): resolve the dead channel in UpdateNewAndDoneWatch (#61795)

[ti-chi-bot]

This is an automated cherry-pick of #61795

What problem does this PR solve?

Issue Number: close #61782.

Problem Summary:

Revert #52283 and implement a simpler method to prevent error logs.

What changed and how does it work?

Check List

Tests

• Unit test
• Integration test
• Manual test (add detailed scripts or steps below)

Mannually modify maxWatchRecordChannelSize to 10 to ensure easier triggering.

Before:

After:

Release note

Please refer to Release Notes Language Style Guide to write a quality release note.

Resolve the issue causing system table read/write operations related to runaways to hang after restarting TiDB instance.

[ti-chi-bot]

@JmPotato This PR has conflicts, I have hold it.
Please resolve them or ask others to resolve them, then comment /unhold to remove the hold label.

[ti-chi-bot]

This cherry pick PR is for a release branch and has not yet been approved by triage owners.
Adding the do-not-merge/cherry-pick-not-approved label.

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[ti-chi-bot]

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[ti-chi-bot]

@ti-chi-bot: The following tests 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-tidb/check_dev_2	c952360	link	true	/test check-dev2
idc-jenkins-ci-tidb/mysql-test	c952360	link	true	/test mysql-test
idc-jenkins-ci-tidb/build	c952360	link	true	/test build
idc-jenkins-ci-tidb/check_dev	c952360	link	true	/test check-dev
idc-jenkins-ci-tidb/unit-test	c952360	link	true	/test unit-test

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