Confidential compute (intel, amd and nvidia) already is a thing and has nothing to do with mozilla. Without such drastic measures, no, it IS impossible with regular cloud processing.
They do have a focus on that, it just hasn't really panned out. To be fair, you're talking about the billion dollar question. It's not exactly an easy problem.
It's called motivated reasoning. "Firefox must suck because I don't want to switch to it", so when firefox buys a bookmarking tool and integrates it into the browser, that's apparently "user hostile", while google wants to force your browser to attest that you haven't blocked any ads.