[1/N][Refactor] Clean up dead code in output processor

[gcanlin]

PLEASE FILL IN THE PR DESCRIPTION HERE ENSURING ALL CHECKLIST ITEMS (AT THE BOTTOM) HAVE BEEN CONSIDERED.

Purpose

Related to #1577. Phase 0 clean the dead code:

• Remove register_handler(), output_handlers dict, and custom handler dispatch (zero callers)
• Remove _reqid_to_mm_type (populated but never read)
• Remove _process_text_image_output (no config uses "text+image")
• Remove _extract_from_multimodal_outputs (eco has no multimodal_outputs attr, always returns None)
• Remove _process_pooling_output (calls torch.as_tensor on a dict — broken)
• Remove _process_text_output (no-op)
• Remove _route_and_normalize and all _process_*_output methods (entire routing layer was a no-op in production)
• Remove dead "model_outputs" fallback in serving_speech.py (key remapping ensures it's always "audio")

Test Plan

Test Result

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Essential Elements of an Effective PR Description Checklist

• The purpose of the PR, such as "Fix some issue (link existing issues this PR will resolve)".
• The test plan. Please provide the test scripts & test commands. Please state the reasons if your codes don't require additional test scripts. For test file guidelines, please check the test style doc
• The test results. Please paste the results comparison before and after, or the e2e results.
• (Optional) The necessary documentation update, such as updating supported_models.md and examples for a new model. Please run mkdocs serve to sync the documentation editions to ./docs.
• (Optional) Release notes update. If your change is user-facing, please update the release notes draft.

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