[PR #10977/48f5324b backport][3.12] Fix flakey test_aiohttp_request_ctx_manager_close_sess_on_error test

[patchback]

This is a backport of PR #10977 as merged into master (48f5324).

SSL cleanup still needs one sleep of the event loop to fully cleanup
on older python versions

[codspeed-hq]

CodSpeed Performance Report

Merging #10980 will not alter performance

_{Comparing patchback/backports/3.12/48f5324bf2b694073a8c66374d7791e736bd9bed/pr-10977 (731c77c) with 3.12 (8368069)}

Summary

✅ 59 untouched benchmarks

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 98.16%. Comparing base (8368069) to head (731c77c).
Report is 1 commits behind head on 3.12.

✅ All tests successful. No failed tests found.

Additional details and impacted files

@@           Coverage Diff           @@
##             3.12   #10980   +/-   ##
=======================================
  Coverage   98.16%   98.16%           
=======================================
  Files         130      130           
  Lines       39754    39755    +1     
  Branches     2241     2241           
=======================================
+ Hits        39025    39026    +1     
  Misses        557      557           
  Partials      172      172           

Flag	Coverage Δ
CI-GHA	98.05% <100.00%> (+<0.01%)	⬆️
OS-Linux	97.77% <100.00%> (+<0.01%)	⬆️
OS-Windows	95.26% <100.00%> (-0.01%)	⬇️
OS-macOS	96.94% <100.00%> (+<0.01%)	⬆️
Py-3.10.11	96.83% <100.00%> (-0.01%)	⬇️
Py-3.10.17	97.38% <100.00%> (+0.01%)	⬆️
Py-3.11.12	97.43% <100.00%> (+<0.01%)	⬆️
Py-3.11.9	96.93% <100.00%> (+<0.01%)	⬆️
Py-3.12.10	97.83% <100.00%> (+<0.01%)	⬆️
Py-3.13.3	97.82% <100.00%> (+<0.01%)	⬆️
Py-3.9.13	96.72% <100.00%> (-0.01%)	⬇️
Py-3.9.22	97.22% <100.00%> (-0.04%)	⬇️
Py-pypy7.3.16	90.11% <100.00%> (+1.39%)	⬆️
VM-macos	96.94% <100.00%> (+<0.01%)	⬆️
VM-ubuntu	97.77% <100.00%> (+<0.01%)	⬆️
VM-windows	95.26% <100.00%> (-0.01%)	⬇️

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