GPT-5.1 Batch

I want you to route my LLM calls for "gpt-5.1-batch" through the Experiential gateway instead of calling the provider directly. It speaks the OpenAI Chat Completions API, so this is a base-URL and key swap. Please:

1. Point the client at https://api-pr-334.preview.experientiallabs.ai/v1 as the base URL.
2. Authenticate with my Experiential API key from the EXPLABS_API_KEY environment variable. If it isn't set, stop and tell me to create one under Settings -> API Keys and export it.
3. Use the model id "gpt-5.1-batch" exactly.
4. Update every place my code builds an LLM client for this model to use that base URL and key, leaving streaming and tool-calls as they are.
5. Make one test call and show me the reply plus the token usage, so we confirm it runs on my Experiential credits.

Tell me which files you changed.