[Inference Providers] Fix structured output schema in chat completion

[hanouticelina]

This PR fixes compatibility issues with structured outputs across providers by ensuring the InferenceClient follows the OpenAI API specs structured output.

Originally raised by @akseljoonas on Slack:

I have been trying out structured outputs through the InferenceClient on the hub's Python package, and I saw that each inference provider (Nebius, Novita, Together, etc) has a slightly different format that they expect for the call with structured output. So I wanted to ask if there is any mapping being done under the hood to match the format of the provider? Im currently passing in the schema below and getting 500 errors with Novita while it works with Nebius
response_format = {
"type": "json_object",
"value": response_format["json_schema"]["schema"],
}

It turns out some providers don’t fully follow OpenAI’s spec for the response_format field. This PR ensures the client always uses the OpenAI-compliant format and adds internal mappings for each provider when needed.

Note: When integrating a new provider into our clients, we should ensure that structured output and function calling are compatible with the OpenAI specs. If that’s not the case, a custom mapping should be added as part of the integration.

[HuggingFaceDocBuilderDev]

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[Wauplin]

Is this PR a follow-up of huggingface/huggingface.js#1380 or are the types added manually ? (just curious)

[hanouticelina]

I added the types manually for now (huggingface/huggingface.js#1380 is more of an experiment and not totally ready to be used). also, i'm not sure it's worth prioritizing the switch to the OpenAPI specs of OpenAI for now.

That said, since we don't do any input validation, adding the new types here is not "necessary", it was mainly to show the discrepancy between TGI and OpenAI specs for structured output.

[Wauplin]

Thanks for working on this! Now I understand better why we are always testing MCP servers on Nebius ^^

[Wauplin]

Haven't tested it myself for all providers but looks good to me! Just a nit regarding removing parameters from the input mapping (not sure it's necessary).

Pre-approving so that I'm not a blocker on this :)