client/pkg: introduce the deadline watcher

[JmPotato]

What problem does this PR solve?

Issue Number: ref #8690.

What is changed and how does it work?

Introduce the deadline watcher.

Check List

Tests

• Unit test
• Integration test

Release note

None.

[ti-chi-bot]

[APPROVALNOTIFIER] This PR is APPROVED

This pull-request has been approved by: lhy1024, rleungx

The full list of commands accepted by this bot can be found here.

The pull request process is described here

Needs approval from an approver in each of these files:

• OWNERS [lhy1024,rleungx]

Approvers can indicate their approval by writing /approve in a comment
Approvers can cancel approval by writing /approve cancel in a comment

[ti-chi-bot]

[LGTM Timeline notifier]

Timeline:

• 2024-12-27 09:07:12.333805993 +0000 UTC m=+82167.689810532: ☑️ agreed by lhy1024.
• 2024-12-31 04:02:11.233293022 +0000 UTC m=+409466.589297591: ☑️ agreed by rleungx.

[codecov]

Codecov Report

Attention: Patch coverage is 84.21053% with 9 lines in your changes missing coverage. Please review.

Project coverage is 76.31%. Comparing base (5999d64) to head (c2e9e9d).
Report is 2 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #8955      +/-   ##
==========================================
+ Coverage   76.22%   76.31%   +0.08%     
==========================================
  Files         464      465       +1     
  Lines       70516    70537      +21     
==========================================
+ Hits        53754    53832      +78     
+ Misses      13407    13355      -52     
+ Partials     3355     3350       -5     

Flag	Coverage Δ
unittests	76.31% <84.21%> (+0.08%)	⬆️

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