fix: refactor reasoning algo

[galzilber]

Important

Refactor reasoning algorithm by consolidating handling across providers, reducing logging, and updating tests.

• Behavior:
  • Consolidated inline reasoning handling across providers; payloads now use a separate reasoning_effort field and token limits are adjusted for provider-specific fields.
  • Reduced runtime logging related to reasoning across Anthropic, Azure, OpenAI, and Vertex AI.
  • Removed deprecated public helpers related to reasoning to simplify the API surface.
• Tests:
  • Updated tests to validate reasoning transformation paths, token/effort behavior, and preservation of existing system messages.

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Summary by CodeRabbit

• Refactor
  • Consolidated inline reasoning handling across providers; payloads now use a separate reasoning_effort field and token limits are adjusted for provider-specific fields.
  • Reduced runtime logging related to reasoning across Anthropic, Azure, OpenAI, and Vertex AI.
  • Removed deprecated public helpers related to reasoning to simplify the API surface.
• Tests
  • Updated tests to validate reasoning transformation paths, token/effort behavior, and preservation of existing system messages.