client/tso: double-check the contexts to prevent waiting for TSO requests in closed chan (#7962)

[ti-chi-bot]

This is an automated cherry-pick of #7962

What problem does this PR solve?

Issue Number: close #7849.

What is changed and how does it work?

This PR ensures that a `tsoRequest` could be done by double-checking the contexts to prevent waiting for TSO requests in the closed channel.

Check List

Tests

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

Release note

None.

[ti-chi-bot]

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[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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