[PR #10003/78d1be5 backport][3.11] Fix client connection header not reflecting connector force_close value

[bdraco]

(cherry picked from commit 78d1be5)

[codspeed-hq]

CodSpeed Performance Report

Merging #10009 will improve performances by 8.71%

_{Comparing patchback/backports/3.11/78d1be5d79f67597313354646eec200ff603fd9d/pr-10003 (3f63185) with 3.11 (b235e76)}

Summary

⚡ 1 improvements
✅ 42 untouched benchmarks

Benchmarks breakdown

	Benchmark	3.11	patchback/backports/3.11/78d1be5d79f67597313354646eec200ff603fd9d/pr-10003	Change
⚡	test_send_client_request_one_hundred[pyloop]	3.1 ms	2.8 ms	+8.71%

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

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✅ All tests successful. No failed tests found.

Additional details and impacted files

@@           Coverage Diff           @@
##             3.11   #10009   +/-   ##
=======================================
  Coverage        ?   98.03%           
=======================================
  Files           ?      122           
  Lines           ?    36889           
  Branches        ?     4440           
=======================================
  Hits            ?    36163           
  Misses          ?      543           
  Partials        ?      183           

Flag	Coverage Δ
CI-GHA	97.92% <100.00%> (?)
OS-Linux	97.63% <100.00%> (?)
OS-Windows	94.52% <100.00%> (?)
OS-macOS	96.74% <100.00%> (?)
Py-3.10.11	96.59% <100.00%> (?)
Py-3.10.15	97.17% <100.00%> (?)
Py-3.11.10	97.20% <100.00%> (?)
Py-3.11.9	96.66% <100.00%> (?)
Py-3.12.7	97.69% <100.00%> (?)
Py-3.13.0	97.64% <100.00%> (?)
Py-3.9.13	96.52% <100.00%> (?)
Py-3.9.20	97.09% <100.00%> (?)
Py-pypy7.3.16	96.66% <100.00%> (?)
VM-macos	96.74% <100.00%> (?)
VM-ubuntu	97.63% <100.00%> (?)
VM-windows	94.52% <100.00%> (?)

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