otelhttp: Remove custom wrapper after handling request

[VirrageS]

Closes #6908

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 75.5%. Comparing base (3ea6585) to head (a971793).

Additional details and impacted files

@@           Coverage Diff           @@
##            main   #6914     +/-   ##
=======================================
- Coverage   75.5%   75.5%   -0.1%     
=======================================
  Files        207     207             
  Lines      19319   19323      +4     
=======================================
+ Hits       14601   14602      +1     
- Misses      4283    4285      +2     
- Partials     435     436      +1     

Files with missing lines	Coverage Δ
instrumentation/net/http/otelhttp/handler.go	93.0% <100.0%> (+0.1%)	⬆️

... and 1 file with indirect coverage changes

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