Probably whoever becomes the default provider for this new function. Like Google pays to be the default search provider.

The technical information is scarce but I very much doubt Mozilla is going to train and deploy their own model. It’s more likely you will get a free tier access to one of the popular commercial offerings - Gemini, ChatGPT, Anthropic … whoever pays for it.

In their defense, Mozilla doesn’t have their own source of income, they heavily depend on search sponsorships. Jumping onto the AI train is one way to keep afloat for now

Did anyone think they would not?
Given enough time it’s inevitable any determined organization could make it.