Modern React development doesn’t deal with these things much not because devs don’t learn web APIs but because most projects use various component libraries that abstract web APIs from devs. You as an app developer do a lot more work to glue components together to achieve the desired behavior and you mostly deal with data management.
I don’t say Remix is bad, it’s an impressive piece of technology for building interactive UIs that tries to blend server side and browser side of web in a neat package, quite successfully I must say! It’s very pleasant to work with, not hard to get into, and I personally haven’t found any big drawbacks. I’d recommend it for all sorts of projects!
But this whole “we do plain web APIs” marketing angle is IMO strange and misleading. Remix is a set of APIs on top of React, you will be building React apps with it, with JSX, hooks and everything else. It’s NOT a vanilla web, far from it.