[PR #10981/2617ab23 backport][3.12] Fix flakey test_client_middleware_retry_reuses_connection test

[patchback]

This is a backport of PR #10981 as merged into master (2617ab2).

Adjust the test instead since #10976 was closed.

Ensure that we always send an empty body on the first response as sending a body will cause the connection to not get reused sometimes.

[codspeed-hq]

CodSpeed Performance Report

Merging #10986 will not alter performance

_{Comparing patchback/backports/3.12/2617ab23d015ed0915f1bccb44774cdbdbce1313/pr-10981 (0fe4297) with 3.12 (bfe0bd1)}

Summary

✅ 59 untouched benchmarks

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 98.16%. Comparing base (bfe0bd1) to head (0fe4297).
Report is 2 commits behind head on 3.12.

✅ All tests successful. No failed tests found.

Additional details and impacted files

@@            Coverage Diff             @@
##             3.12   #10986      +/-   ##
==========================================
+ Coverage   97.88%   98.16%   +0.28%     
==========================================
  Files         130      130              
  Lines       39755    39759       +4     
  Branches     2241     2242       +1     
==========================================
+ Hits        38914    39030     +116     
+ Misses        659      557     -102     
+ Partials      182      172      -10     

Flag	Coverage Δ
CI-GHA	98.05% <100.00%> (+0.26%)	⬆️
OS-Linux	97.77% <100.00%> (+0.01%)	⬆️
OS-Windows	95.26% <100.00%> (?)
OS-macOS	96.94% <100.00%> (+<0.01%)	⬆️
Py-3.10.11	96.83% <100.00%> (+0.27%)	⬆️
Py-3.10.17	97.38% <100.00%> (+<0.01%)	⬆️
Py-3.11.12	97.47% <100.00%> (+0.66%)	⬆️
Py-3.11.9	96.93% <100.00%> (+0.26%)	⬆️
Py-3.12.10	97.83% <100.00%> (+0.24%)	⬆️
Py-3.13.3	97.82% <100.00%> (+0.86%)	⬆️
Py-3.9.13	96.72% <100.00%> (+0.26%)	⬆️
Py-3.9.22	97.26% <100.00%> (+0.62%)	⬆️
Py-pypy7.3.16	93.78% <100.00%> (?)
VM-macos	96.94% <100.00%> (+<0.01%)	⬆️
VM-ubuntu	97.77% <100.00%> (+0.01%)	⬆️
VM-windows	95.26% <100.00%> (?)

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