Ensure websocket transport is closed when client does not close it (#8200)

[bdraco]

(cherry picked from commit 6ec4747)

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 97.40%. Comparing base (6e8f63c) to head (cd2d88a).
Report is 1 commits behind head on 3.9.

Additional details and impacted files

@@            Coverage Diff             @@
##              3.9    #8256      +/-   ##
==========================================
+ Coverage   97.36%   97.40%   +0.03%     
==========================================
  Files         108      108              
  Lines       32639    32731      +92     
  Branches     3874     3874              
==========================================
+ Hits        31780    31880     +100     
+ Misses        655      647       -8     
  Partials      204      204              

Flag	Coverage Δ
CI-GHA	97.31% <100.00%> (+0.03%)	⬆️
OS-Linux	96.99% <98.98%> (+0.02%)	⬆️
OS-Windows	94.69% <100.00%> (+0.01%)	⬆️
OS-macOS	96.81% <98.98%> (+0.03%)	⬆️
Py-3.10.11	94.39% <100.00%> (?)
Py-3.10.13	96.52% <98.98%> (+0.03%)	⬆️
Py-3.10.14	96.74% <98.98%> (+0.22%)	⬆️
Py-3.11.8	96.82% <100.00%> (+0.03%)	⬆️
Py-3.12.2	96.87% <100.00%> (+0.03%)	⬆️
Py-3.8.10	94.37% <100.00%> (+<0.01%)	⬆️
Py-3.8.18	96.71% <98.98%> (+0.03%)	⬆️
Py-3.9.13	94.38% <100.00%> (+0.02%)	⬆️
Py-3.9.18	96.50% <98.98%> (+0.03%)	⬆️
Py-3.9.19	96.72% <98.98%> (+0.03%)	⬆️
Py-pypy7.3.15	96.30% <98.98%> (+0.03%)	⬆️
VM-macos	96.81% <98.98%> (+0.03%)	⬆️
VM-ubuntu	96.99% <98.98%> (+0.02%)	⬆️
VM-windows	94.69% <100.00%> (+0.01%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.