Improve the handling of AI clients and API keys

[jtpio]

We should look into improving how the clients are instantiated, and the API keys provided:

• do we need to instantiate both a MistralAI and ChatMistralAI clients?
• maybe there should be one plugin to provide the AI clients, that other plugins would consume
• offer a way to use in set the API key without going through the settings system, since the settings are stored in the browser in JupyterLite

_Originally posted by @jtpio in https://github.com/jupyterlite/jupyterlab-codestral/pull/6#discussion_r1816217804_

[brichet]

• do we need to instantiate both a MistralAI and ChatMistralAI clients?

They seem to be intended for different uses, respectively completion and chat.

From the API of ChatMistralAI and MistralAI:

• Class ChatMistralAI Mistral AI chat model integration.

• Class MistralAI MistralAI completions LLM.