Rewrite with pydantic-ai

[vrslev]

@xfenix proposed making any-llm-client a lightweight wrapper around pydantic-ai to avoid competition with it. I agree that this is a good idea, as it will clarify the purpose of any-llm-client and reduce the maintenance burden.

I envision this as a thin layer that allows us to configure the LLM using environment variables, enabling us to switch LLMs without changing the code—only the configuration.

To implement this, we need to:

• Add support for YandexGPT,
• Create a custom OpenAI provider that supports request_extra,
• Refactor the code so that any_llm_client.get_client() returns pydantic_ai.Model.
• Add helper that would reraise OutOfTokensOrSymbolsError