Fix cancellations being swallowed (#9030)

[Dreamsorcerer]

Co-authored-by: J. Nick Koston nick@koston.org
(cherry picked from commit 1a77ad9)

[codecov]

Codecov Report

Attention: Patch coverage is 94.44444% with 4 lines in your changes missing coverage. Please review.

Project coverage is 97.78%. Comparing base (76284b5) to head (aa1e66f).
Report is 2 commits behind head on 3.10.

✅ All tests successful. No failed tests found.

Files with missing lines	Patch %	Lines
aiohttp/client_reqrep.py	76.47%	2 Missing and 2 partials ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             3.10    #9258      +/-   ##
==========================================
- Coverage   97.79%   97.78%   -0.01%     
==========================================
  Files         108      108              
  Lines       34745    34797      +52     
  Branches     4150     4157       +7     
==========================================
+ Hits        33979    34027      +48     
  Misses        573      573              
- Partials      193      197       +4     

Flag	Coverage Δ
CI-GHA	97.68% <93.05%> (-0.01%)	⬇️
OS-Linux	97.36% <93.05%> (-0.01%)	⬇️
OS-Windows	94.96% <93.05%> (-0.01%)	⬇️
OS-macOS	97.05% <93.05%> (-0.01%)	⬇️
Py-3.10.11	97.04% <44.44%> (-0.12%)	⬇️
Py-3.10.15	96.97% <44.44%> (-0.12%)	⬇️
Py-3.11.10	96.94% <93.05%> (-0.06%)	⬇️
Py-3.11.9	97.00% <93.05%> (-0.06%)	⬇️
Py-3.12.6	97.40% <93.05%> (-0.01%)	⬇️
Py-3.8.10	94.47% <44.44%> (-0.11%)	⬇️
Py-3.8.18	96.77% <44.44%> (-0.11%)	⬇️
Py-3.9.13	96.95% <44.44%> (-0.11%)	⬇️
Py-3.9.20	96.89% <44.44%> (-0.11%)	⬇️
Py-pypy7.3.16	96.49% <44.44%> (-0.11%)	⬇️
VM-macos	97.05% <93.05%> (-0.01%)	⬇️
VM-ubuntu	97.36% <93.05%> (-0.01%)	⬇️
VM-windows	94.96% <93.05%> (-0.01%)	⬇️

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