[PR #10076/fad44f6b backport][3.11] Fix request count check for BadHttpMethod

[patchback]

This is a backport of PR #10076 as merged into master (fad44f6).

The error handler was incorrectly checking for the first request of the server instead of the first request for the connection

#10055 (comment)

[codspeed-hq]

CodSpeed Performance Report

Merging #10081 will not alter performance

_{Comparing patchback/backports/3.11/fad44f6bc96e4f54a5b8e7e30d1e9e01a021bec9/pr-10076 (7934d75) with 3.11 (a37c4f2)}

Summary

✅ 44 untouched benchmarks

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 98.06%. Comparing base (a37c4f2) to head (7934d75).
Report is 2 commits behind head on 3.11.

✅ All tests successful. No failed tests found.

Additional details and impacted files

@@           Coverage Diff           @@
##             3.11   #10081   +/-   ##
=======================================
  Coverage   98.06%   98.06%           
=======================================
  Files         122      122           
  Lines       37045    37051    +6     
  Branches     4453     4453           
=======================================
+ Hits        36328    36334    +6     
  Misses        540      540           
  Partials      177      177           

Flag	Coverage Δ
CI-GHA	97.95% <100.00%> (+<0.01%)	⬆️
OS-Linux	97.65% <100.00%> (+<0.01%)	⬆️
OS-Windows	94.57% <100.00%> (+<0.01%)	⬆️
OS-macOS	96.77% <100.00%> (+<0.01%)	⬆️
Py-3.10.11	96.63% <100.00%> (+<0.01%)	⬆️
Py-3.10.15	97.17% <100.00%> (-0.05%)	⬇️
Py-3.11.10	97.24% <100.00%> (+<0.01%)	⬆️
Py-3.11.9	96.70% <100.00%> (+<0.01%)	⬆️
Py-3.12.7	97.72% <100.00%> (+<0.01%)	⬆️
Py-3.13.0	97.72% <100.00%> (+0.04%)	⬆️
Py-3.9.13	96.56% <100.00%> (-0.01%)	⬇️
Py-3.9.20	97.13% <100.00%> (+<0.01%)	⬆️
Py-pypy7.3.16	96.71% <100.00%> (+<0.01%)	⬆️
VM-macos	96.77% <100.00%> (+<0.01%)	⬆️
VM-ubuntu	97.65% <100.00%> (+<0.01%)	⬆️
VM-windows	94.57% <100.00%> (+<0.01%)	⬆️

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