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 (a5e8aba) 97.27% compared to head (9682c37) 97.34%.
Report is 1 commits behind head on 3.10.

Additional details and impacted files

@@            Coverage Diff             @@
##             3.10    #7890      +/-   ##
==========================================
+ Coverage   97.27%   97.34%   +0.07%     
==========================================
  Files         108      108              
  Lines       32402    32433      +31     
  Branches     3842     3848       +6     
==========================================
+ Hits        31518    31573      +55     
+ Misses        675      655      -20     
+ Partials      209      205       -4     

Flag	Coverage Δ
CI-GHA	97.25% <100.00%> (+0.06%)	⬆️
OS-Linux	96.95% <100.00%> (+0.07%)	⬆️
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	96.73% <100.00%> (+<0.01%)	⬆️
Py-3.11.6	96.45% <100.00%> (+<0.01%)	⬆️
Py-3.12.0	96.38% <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	96.70% <100.00%> (-0.01%)	⬇️
Py-pypy7.3.13	96.16% <100.00%> (?)
VM-macos	96.76% <100.00%> (+0.20%)	⬆️
VM-ubuntu	96.95% <100.00%> (+0.07%)	⬆️
VM-windows	94.44% <100.00%> (+<0.01%)	⬆️

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