[Refactor] Extract StructuredOutputsParams creation logic from Request.to_sampling_params

[yzong-rh]

Purpose

Add extract_structured_outputs() helpers that normalize a request's StructuredOutputsParams before building sampling params.
Facilitate future Parser.adjust_request() implementation of #48116 and #45560 by consolidating the StructuredOutputsParams extraction logic.

Deduplicate the structured-output normalization logic between the Chat Completions and Completions request paths.

Fix missing json_object support for the Responses API by mapping text.format={"type": "json_object"} into structured outputs.
No other behavioral change.

Test Plan

Unit tests:

.venv/bin/python -m pytest \
  tests/entrypoints/openai/responses/test_sampling_params.py \
  tests/entrypoints/openai/responses/test_serving_responses.py \
  tests/entrypoints/openai/chat_completion/test_chat_error.py \
  tests/entrypoints/openai/completion/test_completion_error.py

.venv/bin/python -m pytest \
  tests/entrypoints/openai/responses/test_structured_output.py \
  tests/entrypoints/openai/chat_completion/test_chat.py \
  tests/entrypoints/openai/completion/test_completion.py \
  tests/tool_use/test_chat_completions.py

Test Result

72 passed, 1 xfailed, 19 warnings

95 passed, 9 skipped, 16 warnings

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• The purpose of the PR, such as "Fix some issue (link existing issues this PR will resolve)".
• The test plan, such as providing test command.
• The test results, such as pasting the results comparison before and after, or e2e results
• (Optional) The necessary documentation update, such as updating supported_models.md and examples for a new model.

[yzong-rh]

cc @bbrowning @chaunceyjiang @arpera

[claude]

Claude Code Review

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[DarkLight1337]

Thanks for the cleanup!

[yzong-rh]

Failure likely unrelated.