Raise error if encountered in chat completion SSE stream

[Wauplin]

Fix #2514 cc @lhoestq @OlivierDehaene

When stream=True is passed, the server response can be HTTP 200 but still get an error as a stream event. We were already parsing them for text_generation task, but not chat_completion. This PR fixes this.

Example

from huggingface_hub import InferenceClient


client = InferenceClient("microsoft/Phi-3-mini-4k-instruct")

for message in client.chat_completion(
    messages=[{"role": "user", "content": "Hello there !"}],
    stream=True,
    max_tokens=4091,  # values lower or equal to 4090 work
):
    print(message.choices[0].delta.content, end="")

Traceback (most recent call last):
  File "/home/wauplin/projects/huggingface_hub/idefi.py", line 6, in <module>
    for message in client.chat_completion(
  File "/home/wauplin/projects/huggingface_hub/src/huggingface_hub/inference/_common.py", line 321, in _stream_chat_completion_response
    output = _format_chat_completion_stream_output(item)
  File "/home/wauplin/projects/huggingface_hub/src/huggingface_hub/inference/_common.py", line 356, in _format_chat_completion_stream_output
    raise _parse_text_generation_error(json_payload["error"], json_payload.get("error_type"))
huggingface_hub.errors.ValidationError: Input validation error: `inputs` tokens + `max_new_tokens` must be <= 4096. Given: 6 `inputs` tokens and 4091 `max_new_tokens`

[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.

[hanouticelina]

LGTM 👍

[Wauplin]

Thanks for the review!