chore(internal): properly set __pydantic_private__

[stainless-app]

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EntelligenceAI PR Summary

A minor update was made to _base_client.py to conditionally initialize __pydantic_private__ when PYDANTIC_V2 is enabled.

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Walkthrough

Minor update in _base_client.py: Added conditional initialization for __pydantic_private__ when PYDANTIC_V2 is true.

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LGTM 👍