[PR #9732/1e911ea backport][3.12] Add Client Middleware Support

[bdraco]

(cherry picked from commit 1e911ea)

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 98.13%. Comparing base (6ea542e) to head (5b59910).
⚠️ Report is 160 commits behind head on 3.12.
✅ All tests successful. No failed tests found.

Additional details and impacted files

@@            Coverage Diff             @@
##             3.12   #10879      +/-   ##
==========================================
+ Coverage   98.09%   98.13%   +0.03%     
==========================================
  Files         126      128       +2     
  Lines       38057    38684     +627     
  Branches     2148     2177      +29     
==========================================
+ Hits        37333    37963     +630     
+ Misses        553      551       -2     
+ Partials      171      170       -1     

Flag	Coverage Δ
CI-GHA	98.02% <100.00%> (+0.04%)	⬆️
OS-Linux	97.75% <100.00%> (+0.04%)	⬆️
OS-Windows	95.19% <100.00%> (+0.08%)	⬆️
OS-macOS	96.91% <100.00%> (+0.06%)	⬆️
Py-3.10.11	96.78% <100.00%> (+0.06%)	⬆️
Py-3.10.17	97.34% <100.00%> (+0.05%)	⬆️
Py-3.11.12	97.40% <100.00%> (+0.05%)	⬆️
Py-3.11.9	96.88% <100.00%> (+0.05%)	⬆️
Py-3.12.10	97.81% <100.00%> (+0.04%)	⬆️
Py-3.13.3	97.76% <100.00%> (+0.01%)	⬆️
Py-3.9.13	96.67% <100.00%> (+0.07%)	⬆️
Py-3.9.22	97.22% <100.00%> (+0.09%)	⬆️
Py-pypy7.3.16	87.21% <100.00%> (+1.57%)	⬆️
VM-macos	96.91% <100.00%> (+0.06%)	⬆️
VM-ubuntu	97.75% <100.00%> (+0.04%)	⬆️
VM-windows	95.19% <100.00%> (+0.08%)	⬆️

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[codspeed-hq]

CodSpeed Performance Report

Merging #10879 will not alter performance

_{Comparing patchback/backports/3.12/1e911eaf23091b42cc374547ff9bf692debf9720/pr-9732 (5b59910) with 3.12 (6ea542e)}

Summary

✅ 60 untouched benchmarks