You said it yourself: a massive swath of Firefox users moved to Firefox specifically because they are trying to avoid AI. Keep it out of the browser; there are plenty of alternatives people would already be using if they wanted AI.
Please don’t. I actively avoid tech that uses Gen AI, since it actively plagiarizes artists to produce inferior “art” and only knows how to give answers people want to hear rather than anything accurate (ex: identifying poisonous mushrooms as edible)...