My experience with React suggests the answer is "not well." (But I'd be happy to be proven wrong on that point!)
From my experience with React, if it's used properly so that the entire component tree isn't rendered every frame, I would expect the overhead of using to be almost nil. You can see in the examples the author using React.memo for this.
(Not without a lot of tricky caching, at least, which has it's own costs).
Not saying this is impractical (Personally, I wouldn't bet on it, but I'm sure it's fine for some things), so much as that the cost model here is fundamentally different.
Regarding React: In many webgl use-cases UI-framework overhead can be neglected as the user interacts either with the scene or the UI rendered by the framework. The browser doesn't usually need to update the DOM and the scene in one frame.