refactor: clean up reasoning implementation

[robinnarsinghranabhat]

Summary

Follow-up cleanups to #5206 (reasoning output in responses API) and #5407 (type fixes), addressing items from mattf's review.

Code changes

• Extracted shared reasoning util (src/llama_stack/providers/utils/inference/reasoning.py): All three providers (vLLM, Ollama, Bedrock) had identical message mapping and chunk wrapping code. Pulled it into a shared reasoning.py util with no defaults -- each provider explicitly passes its field names.

• Simplified return type: openai_chat_completions_with_reasoning is streaming-only across all providers. Removed OpenAIChatCompletionWithReasoning from return type in the API protocol, router, and all provider implementations.

• Removed dead code: Deleted no-op _prepare_reasoning_params stubs from vLLM and Bedrock providers. Inlined Ollama's version (2-line default for reasoning_effort).

• Removed type ignores: Eliminated # type: ignore on _separate_tool_calls assignment (reordered if/else to assign base type first) and on tool_call.index usage in streaming chunk processing.

Test changes:

• Added test_reasoning_basic_streaming and test_reasoning_multi_turn_with_tool_call to the ollama-reasoning test suite.
• Un-skipped vLLM reasoning tests -- the CI action.yaml now configures a reasoning parser, so vLLM actually returns reasoning tokens.

Addressed from review

Item	Status
openai_chat_completions_with_reasoning is streaming only, remove non-streaming return type	Done
Remove unused _prepare_reasoning_params from vLLM	Done
Remove unused _prepare_reasoning_params from Bedrock	Done
Inline _prepare_reasoning_params for Ollama	Done
bedrock, vllm, ollama need same transformations -- consider a util	Done
Put message = OpenAIAssistantMessageParam case first to resolve type ignore	Done
Figure out why there are new type ignores	Done (removed 5 type ignores)
Type of completion_result confused by storing both CC and CC-with-reasoning	Done (removed non-streaming type from union)

TODO ( needs design discussion )

Item	Question
Non-adjacent reasoning items	_get_preceding_reasoning only checks index - 1, based on what I observed from official openai's response output. Is there a missing Edge case ?
Error vs silent fallback	When a user asks for reasoning and the provider doesn't support it, should we return an error or silently proceed without reasoning? Currently falls back silently with a critical log.
Move merge logic to provider	Suggestions Appreciated ...
Gemini implementation	Gemini is strict on input shape and may use different field names (e.g. "thinking"). The shared util now supports custom field names, so this is ready to implement.
n != 1 simplification	Not sure what this means
Reduce model_copy() calls	For safety, currently copying params in multiple places. Need to trace mutation paths to determine redundant copies.
Complete types on _separate_tool_calls	Didn't tamper for now

Test plan

• BFCL Eval maintains accuracy
• vllm server renders prompt correctly with reasoning inside analysis channel
• uv run pre-commit run mypy-full --hook-stage manual --all-files # passes

[mergify]

This pull request has merge conflicts that must be resolved before it can be merged. @robinnarsinghranabhat please rebase it. https://docs.github.com/en/pull-requests/collaborating-with-pull-requests/working-with-forks/syncing-a-fork

[cdoern]

@robinnarsinghranabhat what is the status of this one?

[robinnarsinghranabhat]

@cdoern I might have to rebase. but just awaiting review. But it's mainly effort towards code clean up and get rid of type-ignores for changes introduced in reasoning PR.