I worked on Bromium, and also coauthored what I believe was the first research paper introducing the idea of a browser OS. See https://homes.cs.washington.edu/~levy/tahoma.pdf
Technically, you _can_ add rich OS functionality (such as GUI) on top of sel4 but development will be slow and painful and the performance will be bad. And when done you haven't really improved security that much since most your assets are now outside the tiny kernel.
I believe generally the push has been to better use the isolation feature in existing operating system environments - such as having separate processes for rendering and javascript execution per origin which also have unique sandboxed storage. From a platform vendor as browser vendor perspective, building what amounts to a new operating system running at the hypervisor layer is a huge effort that amounts to them now having one more internal OS to secure.
So I would instead expect this to be more of a research platform task, like perhaps something you would see on Genode.