Document auto route provider selection

[Wauplin]

Document that it's possible to select provider like this:

client.chat.completions.create(
-     model="deepseek-ai/DeepSeek-R1-0528", # automatically select provider based on hf.co/settings/inference-providers
+     model="deepseek-ai/DeepSeek-R1-0528:nebius", # manually select Nebius AI
      ...
)

I removed a lot of mentions to hf.co/settings/inference-providers. It's still valid but I feel that it's a bit niche compared to appending e.g. :groq. In addition to this, all LLM/VLM snippets should be updated in the next hub-docs rebuild (see https://huggingface.co/moonshotai/Kimi-K2-Instruct?inference_api=true&inference_provider=groq&language=python).

[HuggingFaceDocBuilderDev]

The docs for this PR live here. All of your documentation changes will be reflected on that endpoint. The docs are available until 30 days after the last update.

[burtenshaw]

Great improvement! LGTM.

[Wauplin]

Thanks for the quick review :)

[julien-c]

or by going to /settings/inference-providers (i would still showcase it a bit)