refactor: Livechat webhook retry & timeout logic

[dionisio-bot]

Backport of #36793

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Latest commit: 0e6a159

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[codecov]

Codecov Report

❌ Patch coverage is 81.25000% with 3 lines in your changes missing coverage. Please review.
✅ Project coverage is 65.85%. Comparing base (3b03b3f) to head (0e6a159).
⚠️ Report is 2 commits behind head on release-7.10.4.

Additional details and impacted files

@@                Coverage Diff                 @@
##           release-7.10.4   #37433      +/-   ##
==================================================
- Coverage           66.25%   65.85%   -0.40%     
==================================================
  Files                3289     3214      -75     
  Lines              110364   109206    -1158     
  Branches            20913    20605     -308     
==================================================
- Hits                73120    71920    -1200     
- Misses              34565    34669     +104     
+ Partials             2679     2617      -62     

Flag	Coverage Δ
e2e	55.98% <ø> (-1.52%)	⬇️
unit	71.56% <81.25%> (-0.02%)	⬇️

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