[PR #10902/94de3f9d backport][3.12] Middleware cleanups

[patchback]

This is a backport of PR #10902 as merged into master (94de3f9).

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 98.15%. Comparing base (c8c3d5f) to head (7ff39e5).
⚠️ Report is 153 commits behind head on 3.12.
✅ All tests successful. No failed tests found.

Additional details and impacted files

@@            Coverage Diff             @@
##             3.12   #10904      +/-   ##
==========================================
- Coverage   98.15%   98.15%   -0.01%     
==========================================
  Files         130      130              
  Lines       39144    39157      +13     
  Branches     2218     2215       -3     
==========================================
+ Hits        38423    38434      +11     
- Misses        551      552       +1     
- Partials      170      171       +1     

Flag	Coverage Δ
CI-GHA	98.04% <100.00%> (-0.01%)	⬇️
OS-Linux	97.77% <100.00%> (-0.01%)	⬇️
OS-Windows	95.23% <100.00%> (-0.01%)	⬇️
OS-macOS	96.94% <100.00%> (-0.01%)	⬇️
Py-3.10.11	96.81% <100.00%> (-0.01%)	⬇️
Py-3.10.17	97.36% <100.00%> (-0.01%)	⬇️
Py-3.11.12	97.47% <100.00%> (+0.03%)	⬆️
Py-3.11.9	96.91% <100.00%> (-0.01%)	⬇️
Py-3.12.10	97.83% <100.00%> (-0.01%)	⬇️
Py-3.13.3	97.83% <100.00%> (+<0.01%)	⬆️
Py-3.9.13	96.71% <100.00%> (+<0.01%)	⬆️
Py-3.9.22	97.24% <100.00%> (+0.02%)	⬆️
Py-pypy7.3.16	81.79% <100.00%> (-6.21%)	⬇️
VM-macos	96.94% <100.00%> (-0.01%)	⬇️
VM-ubuntu	97.77% <100.00%> (-0.01%)	⬇️
VM-windows	95.23% <100.00%> (-0.01%)	⬇️

Flags with carried forward coverage won't be shown. Click here to find out more.

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[codspeed-hq]

CodSpeed Performance Report

Merging #10904 will not alter performance

_{Comparing patchback/backports/3.12/94de3f9d3785660c5c40aa2c927bbaa48cf1bb33/pr-10902 (7ff39e5) with 3.12 (c8c3d5f)}

Summary

✅ 60 untouched benchmarks