Fix LiteLLM reasoning_content handling

[cnYui]

Summary

• Split structured ThinkingPart content into message.reasoning_content for the LiteLLM provider.
• Keep user-visible TextPart output in message.content without embedding <think>...</think> blocks.
• Preserve reasoning_content when building LiteLLM ModelResponse objects.

Context

The provider previously formatted structured assistant content with format_content_as_string(). For outputs containing ThinkingPart, that produced content like <think>reasoning</think>\nanswer, which made reasoning text appear in message.content and left LiteLLM callers without a clean reasoning_content field.

This is related to #684, but this PR is scoped to the cookbook LiteLLM custom provider rather than the hosted OpenAI-compatible API.

Test Plan

• uv run pytest tinker_cookbook/third_party/litellm/provider_test.py -q
• uv run ruff check tinker_cookbook/third_party/litellm/
• uv run pyright tinker_cookbook/third_party/litellm
• git diff --check HEAD~1..HEAD