Restore async concurrency safety to websocket compressor (#7865)

[bdraco]

Fixes #7859

(cherry picked from commit 86a2396)

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (a049701) 97.34% compared to head (76bd245) 97.34%.
Report is 2 commits behind head on 3.9.

Additional details and impacted files

@@           Coverage Diff           @@
##              3.9    #7889   +/-   ##
=======================================
  Coverage   97.34%   97.34%           
=======================================
  Files         108      108           
  Lines       32402    32433   +31     
  Branches     3842     3848    +6     
=======================================
+ Hits        31542    31573   +31     
  Misses        655      655           
  Partials      205      205           

Flag	Coverage Δ
CI-GHA	97.25% <100.00%> (+<0.01%)	⬆️
OS-Linux	96.95% <100.00%> (+<0.01%)	⬆️
OS-Windows	94.44% <100.00%> (+<0.01%)	⬆️
OS-macOS	96.76% <100.00%> (+0.20%)	⬆️
Py-3.10.11	94.34% <100.00%> (+<0.01%)	⬆️
Py-3.10.13	96.72% <100.00%> (-0.01%)	⬇️
Py-3.11.6	96.48% <100.00%> (+0.03%)	⬆️
Py-3.12.0	96.50% <100.00%> (?)
Py-3.8.10	94.32% <100.00%> (+<0.01%)	⬆️
Py-3.8.18	96.65% <100.00%> (+<0.01%)	⬆️
Py-3.9.13	94.33% <100.00%> (+<0.01%)	⬆️
Py-3.9.18	96.71% <100.00%> (+<0.01%)	⬆️
Py-pypy7.3.13	96.16% <100.00%> (+<0.01%)	⬆️
VM-macos	96.76% <100.00%> (+0.20%)	⬆️
VM-ubuntu	96.95% <100.00%> (+<0.01%)	⬆️
VM-windows	94.44% <100.00%> (+<0.01%)	⬆️

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