Going through middle layers has pros and cons. You'll likely find better docs and experience by going through the official APIs directly. Maybe start with OpenAI and/or Claude official libraries, both provide pretty good docs.
If you really must use a wrapper, a strategy I use is to look into open-source apps I like and see what they are using. Aider for instance seems to be using this "litellm" thing... If I were to need cross API support for AI, I would probably look into that [1]. llm uses opeanai directly [2]. Etc, etc.
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1: https://github.com/Aider-AI/aider/blob/e76704e261647348fd7c1...
2: https://github.com/simonw/llm/blob/d654c9521235a737e59a4f1d7...