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 (e3b7cbe) 97.37% compared to head (e043857) 97.32%.

Additional details and impacted files

@@            Coverage Diff             @@
##              3.9    #7979      +/-   ##
==========================================
- Coverage   97.37%   97.32%   -0.06%     
==========================================
  Files         108      108              
  Lines       32446    32471      +25     
  Branches     3843     3846       +3     
==========================================
+ Hits        31594    31601       +7     
- Misses        651      664      +13     
- Partials      201      206       +5     

Flag	Coverage Δ
CI-GHA	97.24% <100.00%> (-0.05%)	⬇️
OS-Linux	96.92% <100.00%> (-0.06%)	⬇️
OS-Windows	94.47% <100.00%> (+<0.01%)	⬆️
OS-macOS	96.51% <100.00%> (-0.28%)	⬇️
Py-3.10.11	94.37% <100.00%> (+<0.01%)	⬆️
Py-3.10.13	96.77% <100.00%> (+0.02%)	⬆️
Py-3.11.6	?
Py-3.11.7	96.49% <100.00%> (+0.01%)	⬆️
Py-3.12.0	?
Py-3.12.1	96.55% <100.00%> (+0.01%)	⬆️
Py-3.8.10	94.35% <100.00%> (+<0.01%)	⬆️
Py-3.8.18	96.70% <100.00%> (+0.01%)	⬆️
Py-3.9.13	94.36% <100.00%> (+<0.01%)	⬆️
Py-3.9.18	96.72% <100.00%> (-0.02%)	⬇️
Py-pypy7.3.13	?
VM-macos	96.51% <100.00%> (-0.28%)	⬇️
VM-ubuntu	96.92% <100.00%> (-0.06%)	⬇️
VM-windows	94.47% <100.00%> (+<0.01%)	⬆️

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