I think the control should be in the hands of the public. Stewarded by a public organization with government funds. What do you think?
I don't know. I think today the EU could set up EUBrowser, a fork of Chromium, and start work. Almost all the hard work has been done by OSS contributions. Google engineers, and Google-funded things such as Firefox. They could live off that comfortably while providing a more locked-down browser if they liked.
A more meaningful, less parasitic option would take longer: the EU (or whomoever) writes a browser from scratch. Then they could decide exactly what goes into it, and have independent input into standards etc.
It’d be neat if the EU picked up the torch here but with any government it seems like it’d be better to have a non-profit get a block grant so you avoid things like those salary issues or other challenges: for example, if the EU decided they didn’t want to depend on the U.S. for critical infrastructure, funding a back-to-its-roots Mozilla.org would make it easier for, say, Canada or India to join in without the issues you’d have trying to directly pay government employee salaries.