[PR #10915/545783b backport][3.12] Fix connection reuse for file-like data payloads

[bdraco]

(cherry picked from commit 545783b)

[codspeed-hq]

CodSpeed Performance Report

Merging #10931 will not alter performance

_{Comparing patchback/backports/3.12/545783b9e91c69d48ffd3b85c7eb13d1b19eb55e/pr-10915 (cd1e9a4) with 3.12 (10f0cf8)}

Summary

✅ 59 untouched benchmarks

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 98.16%. Comparing base (10f0cf8) to head (cd1e9a4).
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   #10931      +/-   ##
==========================================
+ Coverage   98.15%   98.16%   +0.01%     
==========================================
  Files         130      130              
  Lines       39304    39652     +348     
  Branches     2223     2240      +17     
==========================================
+ Hits        38577    38925     +348     
- Misses        554      555       +1     
+ Partials      173      172       -1     

Flag	Coverage Δ
CI-GHA	98.05% <100.00%> (+0.01%)	⬆️
OS-Linux	97.78% <100.00%> (+0.01%)	⬆️
OS-Windows	95.26% <100.00%> (+0.04%)	⬆️
OS-macOS	96.95% <99.75%> (+0.01%)	⬆️
Py-3.10.11	96.83% <99.75%> (+0.02%)	⬆️
Py-3.10.17	97.38% <100.00%> (+0.02%)	⬆️
Py-3.11.12	97.44% <100.00%> (-0.02%)	⬇️
Py-3.11.9	96.93% <99.75%> (+0.02%)	⬆️
Py-3.12.10	97.84% <100.00%> (+0.01%)	⬆️
Py-3.13.3	97.83% <100.00%> (+0.02%)	⬆️
Py-3.9.13	96.72% <99.75%> (+0.01%)	⬆️
Py-3.9.22	97.26% <100.00%> (+0.03%)	⬆️
Py-pypy7.3.16	88.75% <99.75%> (+4.46%)	⬆️
VM-macos	96.95% <99.75%> (+0.01%)	⬆️
VM-ubuntu	97.78% <100.00%> (+0.01%)	⬆️
VM-windows	95.26% <100.00%> (+0.04%)	⬆️

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