[PR #8660/14d5295 backport][3.10] Improve performance of WebSockets when there is no timeout

[bdraco]

(cherry picked from commit 14d5295)

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 97.71%. Comparing base (1bc8d53) to head (aec2d1e).
Report is 199 commits behind head on 3.10.

Additional details and impacted files

@@            Coverage Diff             @@
##             3.10    #8663      +/-   ##
==========================================
+ Coverage   97.21%   97.71%   +0.49%     
==========================================
  Files         108      108              
  Lines       33965    33976      +11     
  Branches     4033     4046      +13     
==========================================
+ Hits        33020    33200     +180     
+ Misses        719      579     -140     
+ Partials      226      197      -29     

Flag	Coverage Δ
CI-GHA	97.61% <100.00%> (+0.45%)	⬆️
OS-Linux	97.29% <100.00%> (+0.45%)	⬆️
OS-Windows	94.81% <ø> (?)
OS-macOS	96.96% <100.00%> (+0.09%)	⬆️
Py-3.10.11	97.06% <87.50%> (+0.31%)	⬆️
Py-3.10.14	97.01% <87.50%> (?)
Py-3.11.9	97.24% <87.50%> (+0.58%)	⬆️
Py-3.12.4	97.34% <87.50%> (+0.29%)	⬆️
Py-3.8.10	94.43% <ø> (?)
Py-3.8.18	96.79% <100.00%> (?)
Py-3.9.13	96.94% <100.00%> (?)
Py-3.9.19	96.90% <100.00%> (?)
Py-pypy7.3.16	96.48% <100.00%> (?)
VM-macos	96.96% <100.00%> (+0.09%)	⬆️
VM-ubuntu	97.29% <100.00%> (+0.45%)	⬆️
VM-windows	94.81% <ø> (?)

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