To give credit where it is due, the codepen is not mine, but from this page: https://r3f.docs.pmnd.rs/getting-started/examples from @react-three/fiber.

My guess, and only a guess, is that 3D is especially (only?) useful for navigation. As in moving around documents, panes, windows, etc.

As for "I wonder what it would feel like to use a whole note-taking app ..." The note taking is in some ways already done pretty well. So my current guess is that it is more the navigation that would benefit.

I don't really have answers, but I often feel like I live in 'flatland' these days.

I think it makes sense to go to 3D with a VR headset. But screens are fundamentally flat, and I feel like going to 3D on a screen takes an initial hit in experience. You can reclaim that hit by putting in work, of course.