*: fix context usage when watch etcd

[rleungx]

What problem does this PR solve?

Issue Number: Close #7807

What is changed and how does it work?

Check List

Tests

• Manual test

Use playground to start 3 TiDB, and kill one by one, the watch goroutines are reduced.

Release note

None.

[ti-chi-bot]

[REVIEW NOTIFICATION]

This pull request has been approved by:

• CabinfeverB
• HuSharp

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[CabinfeverB]

Please also modify WatchGlobalConfig

[codecov]

Codecov Report

Merging #7806 (f6aa9bc) into master (12d75c7) will decrease coverage by 0.13%.
The diff coverage is 33.33%.

❗ Current head f6aa9bc differs from pull request most recent head d19d4a5. Consider uploading reports for the commit d19d4a5 to get more accurate results

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #7806      +/-   ##
==========================================
- Coverage   73.50%   73.37%   -0.13%     
==========================================
  Files         432      432              
  Lines       47838    47842       +4     
==========================================
- Hits        35163    35104      -59     
- Misses       9636     9692      +56     
- Partials     3039     3046       +7     

Flag	Coverage Δ
unittests	73.37% <33.33%> (-0.13%)	⬇️

Flags with carried forward coverage won't be shown. Click here to find out more.

[rleungx]

/merge

[ti-chi-bot]

@rleungx: It seems you want to merge this PR, I will help you trigger all the tests:

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[ti-chi-bot]

This pull request has been accepted and is ready to merge.

Commit hash: f6aa9bc

[ti-chi-bot]

@rleungx: Your PR was out of date, I have automatically updated it for you.

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[ti-chi-bot]

In response to a cherrypick label: new pull request created to branch release-7.5: #7811.

[ti-chi-bot]

In response to a cherrypick label: new pull request created to branch release-7.1: #7813.