I've set browser.ml.chat.provider to http://localhost:8080/ to use the feature with Ollama and that works fine. Perhaps it's not difficult to add support for websites like Groq?
I've tried changing the URL to chat.groq.com but it appears Firefox doesn't know how to submit the prompt. I haven't dug into it very deeply, but I feel like it should work after a rather minor change on either Firefox's end or Groq's end.