[PR #9671/37d9fe6 backport][3.11] Refactor connection waiters to be cancellation safe

[bdraco]

(cherry picked from commit 37d9fe6)

[codspeed-hq]

CodSpeed Performance Report

Merging #9675 will not alter performance

_{Comparing patchback/backports/3.11/37d9fe68387e3672604ff5b183f48538bca34f16/pr-9671 (392f170) with 3.11 (262fb12)}

Summary

✅ 13 untouched benchmarks

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 97.90%. Comparing base (262fb12) to head (392f170).
Report is 2 commits behind head on 3.11.

✅ All tests successful. No failed tests found.

Additional details and impacted files

@@           Coverage Diff            @@
##             3.11    #9675    +/-   ##
========================================
  Coverage   97.89%   97.90%            
========================================
  Files         117      117            
  Lines       35559    35673   +114     
  Branches     4264     4277    +13     
========================================
+ Hits        34811    34926   +115     
  Misses        559      559            
+ Partials      189      188     -1     

Flag	Coverage Δ
CI-GHA	97.79% <100.00%> (+<0.01%)	⬆️
OS-Linux	97.48% <100.00%> (+0.01%)	⬆️
OS-Windows	94.40% <100.00%> (+0.02%)	⬆️
OS-macOS	96.69% <100.00%> (+0.01%)	⬆️
Py-3.10.11	96.55% <99.63%> (+0.01%)	⬆️
Py-3.10.15	96.98% <99.63%> (+0.01%)	⬆️
Py-3.11.10	97.05% <100.00%> (+0.01%)	⬆️
Py-3.11.9	96.64% <100.00%> (+0.02%)	⬆️
Py-3.12.7	97.52% <100.00%> (+0.01%)	⬆️
Py-3.13.0	97.51% <100.00%> (+0.01%)	⬆️
Py-3.9.13	96.47% <100.00%> (+0.01%)	⬆️
Py-3.9.20	96.90% <100.00%> (+0.01%)	⬆️
Py-pypy7.3.16	96.51% <100.00%> (+0.01%)	⬆️
VM-macos	96.69% <100.00%> (+0.01%)	⬆️
VM-ubuntu	97.48% <100.00%> (+0.01%)	⬆️
VM-windows	94.40% <100.00%> (+0.02%)	⬆️

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[bdraco]

Ran the reproducer against this and its confirmed fixed

[bdraco]

Looks like the PR volume overloaded RTD.

Will close reopen to get another run