fix: extension backend dispatch

[zirain]

fixes: #10255

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[chatgpt-codex-connector]

Codex Review Summary

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Review	Status	Commit	Review trigger
📝 Code Review	✅ Completed 2026-10-13T03:52:59.654034Z	c5ab11f	New commits

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Reviewed commit: 681d6e0365

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[codecov]

Codecov Report

❌ Patch coverage is 91.37931% with 5 lines in your changes missing coverage. Please review.
✅ Project coverage is 81.61%. Comparing base (f74a274) to head (c5ab11f).
⚠️ Report is 2 commits behind head on main.

Files with missing lines	Patch %	Lines
internal/gatewayapi/runner/runner.go	0.00%	5 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main   #10256      +/-   ##
==========================================
+ Coverage   81.59%   81.61%   +0.01%     
==========================================
  Files         266      266              
  Lines       41654    41676      +22     
==========================================
+ Hits        33989    34014      +25     
+ Misses       7664     7661       -3     
  Partials        1        1              

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Reviewed commit: f808e4255d

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