Add PublicAI provider

[Wauplin]

Related to huggingface/huggingface.js#1743

Tested on https://huggingface.co/swiss-ai/Apertus-70B-Instruct-2509:

from huggingface_hub import InferenceClient

client = InferenceClient(provider="publicai")
completion = client.chat.completions.create(
    model="swiss-ai/Apertus-70B-Instruct-2509",
    messages=[{"role": "user", "content": "What is the capital of Switzerland?"}],
)

print(completion.choices[0].message.content)

The capital of Switzerland is Bern. 

As an AI, I don't know the date, but according to my knowledge cutoff date of 2024-04, Bern remains the capital of Switzerland.

[HuggingFaceDocBuilderDev]

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