fix: move reasoning wrapper types to llama-stack-api and fix mypy errors

[cdoern]

What does this PR do?

PR #5206 merged with openai_chat_completions_with_reasoning returning -> object which hid type errors. The wrapper types OpenAIChatCompletionWithReasoning and OpenAIChatCompletionChunkWithReasoning were incorrectly placed in providers/inline/responses/builtin/responses/types.py instead of being in llama-stack-api where API types belong.

This change:

• Moves the wrapper types to src/llama_stack_api/inference/models.py
• Converts them from @DataClass to BaseModel with Field() descriptors to match the rest of the API model definitions
• Updates all imports across providers (bedrock, ollama, vllm) and routers
• Adds explicit type annotation for completion_result variable that can hold either regular or reasoning-aware completion types
• Fixes mypy errors that were previously hidden by the -> object return type

[github-actions]

✱ Stainless preview builds

This PR will update the llama-stack-client SDKs with the following commit message.

fix: move reasoning wrapper types to llama-stack-api and fix mypy errors

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Last updated: 2026-04-01 18:22:30 UTC

[skamenan7]

LGTM, apart couple of comments.

[robinnarsinghranabhat]

Just reassuring to know that BFCL eval results remain consistent with #5206