[PR #9671/37d9fe6 backport][3.10] Refactor connection waiters to be cancellation safe

[bdraco]

(cherry picked from commit 37d9fe6)

[codspeed-hq]

CodSpeed Performance Report

Merging #9674 will not alter performance

_{Comparing patchback/backports/3.10/37d9fe68387e3672604ff5b183f48538bca34f16/pr-9671 (63b78a0) with 3.10 (e141032)}

Summary

✅ 13 untouched benchmarks

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 97.86%. Comparing base (e141032) to head (63b78a0).
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    #9674    +/-   ##
========================================
  Coverage   97.85%   97.86%            
========================================
  Files         112      112            
  Lines       35329    35439   +110     
  Branches     4248     4261    +13     
========================================
+ Hits        34572    34683   +111     
  Misses        564      564            
+ Partials      193      192     -1     

Flag	Coverage Δ
CI-GHA	97.75% <100.00%> (+<0.01%)	⬆️
OS-Linux	97.44% <100.00%> (+0.01%)	⬆️
OS-Windows	95.01% <100.00%> (+0.01%)	⬆️
OS-macOS	97.15% <100.00%> (+0.01%)	⬆️
Py-3.10.11	97.00% <99.61%> (+0.01%)	⬆️
Py-3.10.15	96.94% <99.61%> (+0.01%)	⬆️
Py-3.11.10	97.01% <100.00%> (+<0.01%)	⬆️
Py-3.11.9	97.09% <100.00%> (+0.02%)	⬆️
Py-3.12.7	97.48% <100.00%> (+0.01%)	⬆️
Py-3.13.0	97.46% <100.00%> (+0.01%)	⬆️
Py-3.8.10	94.40% <100.00%> (+0.02%)	⬆️
Py-3.8.18	96.74% <100.00%> (+0.01%)	⬆️
Py-3.9.13	96.91% <100.00%> (+<0.01%)	⬆️
Py-3.9.20	96.86% <100.00%> (+0.01%)	⬆️
Py-pypy7.3.16	96.46% <100.00%> (+0.01%)	⬆️
VM-macos	97.15% <100.00%> (+0.01%)	⬆️
VM-ubuntu	97.44% <100.00%> (+0.01%)	⬆️
VM-windows	95.01% <100.00%> (+0.01%)	⬆️

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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