[PR #9340/8a97e03 backport][3.11] Use dunder writer internally in ClientResponse

[bdraco]

(cherry picked from commit 8a97e03)

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 97.79%. Comparing base (e1890ae) to head (1cc239a).
Report is 357 commits behind head on 3.11.

✅ All tests successful. No failed tests found.

Additional details and impacted files

@@            Coverage Diff             @@
##             3.11    #9342      +/-   ##
==========================================
- Coverage   97.80%   97.79%   -0.01%     
==========================================
  Files         108      108              
  Lines       35014    35014              
  Branches     4180     4180              
==========================================
- Hits        34245    34243       -2     
- Misses        573      574       +1     
- Partials      196      197       +1     

Flag	Coverage Δ
CI-GHA	97.67% <100.00%> (-0.01%)	⬇️
OS-Linux	97.36% <100.00%> (-0.01%)	⬇️
OS-Windows	94.94% <100.00%> (-0.01%)	⬇️
OS-macOS	97.06% <100.00%> (-0.01%)	⬇️
Py-3.10.11	96.93% <100.00%> (-0.01%)	⬇️
Py-3.10.15	96.86% <100.00%> (-0.01%)	⬇️
Py-3.11.10	96.93% <100.00%> (-0.01%)	⬇️
Py-3.11.9	97.00% <100.00%> (-0.01%)	⬇️
Py-3.12.6	97.40% <100.00%> (-0.01%)	⬇️
Py-3.13.0-rc.2	97.38% <100.00%> (-0.01%)	⬇️
Py-3.9.13	96.84% <100.00%> (-0.01%)	⬇️
Py-3.9.20	96.78% <100.00%> (-0.01%)	⬇️
Py-pypy7.3.16	96.38% <100.00%> (-0.01%)	⬇️
VM-macos	97.06% <100.00%> (-0.01%)	⬇️
VM-ubuntu	97.36% <100.00%> (-0.01%)	⬇️
VM-windows	94.94% <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.