br/operator: fix stuck when terminating (#52264)

[ti-chi-bot]

This is an automated cherry-pick of #52264

What problem does this PR solve?

Issue Number: close #52243

Problem Summary:
When exiting due to error, we are waiting from the client to finish before receiving from the output channel. In this case, the output channel may be full and blocks the exit procedure.

What changed and how does it work?

We will poll from both the request exit result and the exit channel.

Check List

Tests

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

  • I checked and no code files have been changed.

Side effects

• Performance regression: Consumes more CPU
• Performance regression: Consumes more Memory
• Breaking backward compatibility

Documentation

• Affects user behaviors
• Contains syntax changes
• Contains variable changes
• Contains experimental features
• Changes MySQL compatibility

Release note

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

Fixed an issue where init pod may get stuck when encountering connective errors.

[ti-chi-bot]

[APPROVALNOTIFIER] This PR is NOT APPROVED

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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/build	e408512	link	true	/test build
idc-jenkins-ci-tidb/unit-test	e408512	link	true	/test unit-test
idc-jenkins-ci-tidb/check_dev_2	e408512	link	true	/test check-dev2
idc-jenkins-ci-tidb/check_dev	e408512	link	true	/test check-dev
idc-jenkins-ci-tidb/mysql-test	e408512	link	true	/test mysql-test

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[YuJuncen]

should be picked in #53027