Middleware cleanups

[bdraco]

This is a followup to #9732 to do some small cleanups

• Open discussion point Add Client Middleware Support #9732 (comment)

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 98.75%. Comparing base (a4be2cb) to head (cd9c2b7).
⚠️ Report is 507 commits behind head on master.
✅ All tests successful. No failed tests found.

Additional details and impacted files

@@            Coverage Diff             @@
##           master   #10902      +/-   ##
==========================================
- Coverage   98.75%   98.75%   -0.01%     
==========================================
  Files         129      129              
  Lines       38938    38951      +13     
  Branches     2164     2161       -3     
==========================================
+ Hits        38454    38465      +11     
- Misses        336      337       +1     
- Partials      148      149       +1     

Flag	Coverage Δ
CI-GHA	98.63% <100.00%> (-0.01%)	⬇️
OS-Linux	98.34% <100.00%> (-0.01%)	⬇️
OS-Windows	96.50% <100.00%> (-0.01%)	⬇️
OS-macOS	97.48% <100.00%> (-0.01%)	⬇️
Py-3.10.11	97.38% <100.00%> (-0.01%)	⬇️
Py-3.10.17	97.91% <100.00%> (-0.01%)	⬇️
Py-3.11.12	97.99% <100.00%> (-0.01%)	⬇️
Py-3.11.9	97.47% <100.00%> (+<0.01%)	⬆️
Py-3.12.10	98.41% <100.00%> (-0.02%)	⬇️
Py-3.13.3	98.40% <100.00%> (+<0.01%)	⬆️
Py-3.9.13	97.25% <100.00%> (-0.01%)	⬇️
Py-3.9.22	97.74% <100.00%> (-0.04%)	⬇️
Py-pypy7.3.16	88.30% <100.00%> (-0.89%)	⬇️
VM-macos	97.48% <100.00%> (-0.01%)	⬇️
VM-ubuntu	98.34% <100.00%> (-0.01%)	⬇️
VM-windows	96.50% <100.00%> (-0.01%)	⬇️

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[codspeed-hq]

CodSpeed Performance Report

Merging #10902 will not alter performance

_{Comparing middleware_cleanup (cd9c2b7) with master (a4be2cb)}

Summary

✅ 60 untouched benchmarks

[bdraco]

#9732 (comment) remains an open discussion item. I will address in a future PR if we need to change it.

[patchback]

Backport to 3.12: 💚 backport PR created

✅ Backport PR branch: patchback/backports/3.12/94de3f9d3785660c5c40aa2c927bbaa48cf1bb33/pr-10902

Backported as #10904

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