[PR #9405/b96b01b backport][3.10] Only create the connection closed exception once

[bdraco]

(cherry picked from commit b96b01b)

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 97.79%. Comparing base (e1320b7) to head (41bbb0f).
Report is 2 commits behind head on 3.10.

✅ All tests successful. No failed tests found.

Additional details and impacted files

@@            Coverage Diff             @@
##             3.10    #9410      +/-   ##
==========================================
+ Coverage   97.02%   97.79%   +0.76%     
==========================================
  Files         106      108       +2     
  Lines       34879    34950      +71     
  Branches     4154     4180      +26     
==========================================
+ Hits        33842    34180     +338     
+ Misses        801      573     -228     
+ Partials      236      197      -39     

Flag	Coverage Δ
CI-GHA	97.68% <100.00%> (+0.71%)	⬆️
OS-Linux	97.36% <100.00%> (?)
OS-Windows	94.99% <100.00%> (?)
OS-macOS	97.05% <100.00%> (+0.08%)	⬆️
Py-3.10.11	96.92% <100.00%> (+0.30%)	⬆️
Py-3.10.15	96.86% <100.00%> (?)
Py-3.11.10	96.94% <100.00%> (?)
Py-3.11.9	97.01% <100.00%> (+0.31%)	⬆️
Py-3.12.6	97.40% <100.00%> (?)
Py-3.13.0-rc.3	97.38% <100.00%> (+0.54%)	⬆️
Py-3.8.10	94.37% <100.00%> (?)
Py-3.8.18	96.65% <100.00%> (?)
Py-3.9.13	96.83% <100.00%> (?)
Py-3.9.20	96.77% <100.00%> (?)
Py-pypy7.3.16	96.38% <100.00%> (?)
VM-macos	97.05% <100.00%> (+0.08%)	⬆️
VM-ubuntu	97.36% <100.00%> (?)
VM-windows	94.99% <100.00%> (?)

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