[Feature request] Enable API token for custom `MODEL_ENDPOINT_URL`

If `MODEL_ENDPOINT_URL=http://litellm:4000/` is set but the OpenAI-compatible endpoint expects an API key, there's no way to insert it except to use the `HF_TOKEN`. This would work, however it disables other authentication points to HF services, giving errors like

> ❌ [buildWebSearchQueries] Error generating search queries: InferenceClientProviderApiError: Failed to perform inference: Couldn't authenticate. Reason: Unable authenticate
at innerRequest (file:///usr/src/app/node_modules/.pnpm/@huggingface+inference@4.4.0/node_modules/@huggingface/inference/dist/esm/utils/request.js:45:23)
at process.processTicksAndRejections (node:internal/process/task_queues:105:5)
at async chatCompletion (file:///usr/src/app/node_modules/.pnpm/@huggingface+inference@4.4.0/node_modules/@huggingface/inference/dist/esm/tasks/nlp/chatCompletion.js:10:32)
at async yl (file:///usr/src/app/server/@qwik-city-plan.js:250:358)
at async zp (file:///usr/src/app/server/@qwik-city-plan.js:251:452)
at async qp (file:///usr/src/app/server/@qwik-city-plan.js:235:15488)
at async Hp (file:///usr/src/app/server/@qwik-city-plan.js:235:16045)
at async Qp (file:///usr/src/app/server/@qwik-city-plan.js:235:16471)
at async Wt (file:///usr/src/app/server/@qwik-city-plan.js:235:13059)
at async Object. (file:///usr/src/app/server/@qwik-city-plan.js:251:1728) {
httpRequest: {
url: 'https://api.studio.nebius.ai/v1/chat/completions',
method: 'POST',
headers: {
Authorization: 'Bearer [redacted]',
'Content-Type': 'application/json',
'User-Agent': '@huggingface/inference/4.4.0 Node.js/22'
},
body: {
messages: [Array],
model: 'meta-llama/Llama-3.3-70B-Instruct-fast'
}
},
httpResponse: {
requestId: '5ebfe1aefb7967f2da2107db0db6d16c',
status: 401,
body: { detail: "Couldn't authenticate. Reason: Unable authenticate" }
}
}

A good solution would be to add a `MODEL_ENDPOINT_API_TOKEN` env var

Start by tracing where MODEL_ENDPOINT_URL and HF_TOKEN are read and passed into the OpenAI-compatible and Hugging Face inference paths. Add support for a separate MODEL_ENDPOINT_API_TOKEN, then verify custom endpoint authentication works without changing authentication for HF services.

Written by the indexing model from the issue text.