tso: fix tso proxy error propagation and add test (#9268)

[ti-chi-bot]

This is an automated cherry-pick of #9268

What problem does this PR solve?

Issue Number: ref #9188

What is changed and how does it work?

#9219 fixed error propagation, but had a bug that it propagates an error only for the first request on the stream. This PR fixes the bug and adds test coverage.

Check List

Tests

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

Code changes

• Has the configuration change
• Has HTTP API interfaces changed (Don't forget to add the declarative for the new API)
• Has persistent data change

Side effects

• Possible performance regression
• Increased code complexity
• Breaking backward compatibility

Related changes

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

Release note

None.

[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.

To merge this cherry pick:

1. It must be approved by the approvers firstly.
2. AFTER it has been approved by approvers, please wait for the cherry-pick merging approval from triage owners.

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[ti-chi-bot]

[APPROVALNOTIFIER] This PR is NOT APPROVED

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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	b29ff06	link	true	/test build

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[bufferflies]

no need