The SerenityOS browser! /s kinda

If a dedicated team wanted to work on it, there is the Servo engine which is currently developed by The Linux Foundation but is apparently entirely volunteer driven.

I'm not smart enough to do this kinda shit, but I'm sure there are plenty of others who would gladly work on it to make it bigger than it already is. You could then make your own browser based on that engine. Sure it would take years if not closer to over a decade, but the payoff for privacy and free web would be enough to make me spend all that time doing it.