Fix websocket connection leak (#7978)

[bdraco]

(cherry picked from commit 6f1c608)

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (8222403) 97.37% compared to head (53249db) 97.39%.
Report is 1 commits behind head on 3.10.

Additional details and impacted files

@@            Coverage Diff             @@
##             3.10    #7980      +/-   ##
==========================================
+ Coverage   97.37%   97.39%   +0.02%     
==========================================
  Files         108      108              
  Lines       32541    32564      +23     
  Branches     3847     3850       +3     
==========================================
+ Hits        31687    31716      +29     
+ Misses        652      645       -7     
- Partials      202      203       +1     

Flag	Coverage Δ
CI-GHA	97.30% <100.00%> (+0.02%)	⬆️
OS-Linux	96.99% <100.00%> (+0.02%)	⬆️
OS-Windows	94.48% <100.00%> (+<0.01%)	⬆️
OS-macOS	96.81% <100.00%> (+0.21%)	⬆️
Py-3.10.11	94.39% <100.00%> (+<0.01%)	⬆️
Py-3.10.13	96.77% <100.00%> (+0.02%)	⬆️
Py-3.11.6	96.39% <100.00%> (?)
Py-3.11.7	96.50% <100.00%> (+0.02%)	⬆️
Py-3.12.0	96.44% <100.00%> (?)
Py-3.12.1	96.56% <100.00%> (+0.02%)	⬆️
Py-3.8.10	94.36% <100.00%> (+<0.01%)	⬆️
Py-3.8.18	96.71% <100.00%> (+0.02%)	⬆️
Py-3.9.13	94.37% <100.00%> (+<0.01%)	⬆️
Py-3.9.18	96.76% <100.00%> (+0.02%)	⬆️
Py-pypy7.3.13	96.30% <100.00%> (+0.02%)	⬆️
VM-macos	96.81% <100.00%> (+0.21%)	⬆️
VM-ubuntu	96.99% <100.00%> (+0.02%)	⬆️
VM-windows	94.48% <100.00%> (+<0.01%)	⬆️

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