"There may be a day when everything is in the browser, but that's so far off that it's too early to start focusing on that. What will that look like? How will it work? How does it relate to GNOME, as we currently understand it?"
My guess is that in 10 years, "the browser" will be a very different thing than it is now. But, as your questions imply, it's not possible now to know what "the browser" will be at that time. But I think some educated guesses can be made. I suppose that those who guess right and act on their guesses will tend to be the ones who win out in the future. (And, hopefully, FOSS developers and proponents will be among those who guessed right.)