What do you mean by “browser toolkit”? If you mean “thing that people make web apps with” (like React or like you might imagine Qt being, though it’s not for the web platform), there is not a chance that this will happen by 2025. Zero.
For starters, Rust: Rust is just too complex to be the most popular language when something like JavaScript exists which is faster and easier to get started with, and generally good enough. It has niche usage and will steadily grow, but it’s not going to take over the space any time soon, and probably never will. I say this as a Rust developer for seven years and a web developer for more than fifteen years.
Then the other part, discarding the DOM altogether: there are way too many pieces of functionality that the browser provides that currently cannot be implemented in web user space, for this to become mainstream any time soon. For example: correct scrolling, standard keyboard and mouse event handling, and accessibility. The idea that you would go from quite a few pieces of major functionality completely non-existent in browsers and specs (most of these issues aren’t even being talked about) to mastery of the space within five years is unreasonable.
For further shared abstractions, many web APIs are developed and continue to be developed. Other experiments like WASI exist. WebAssembly has scope to be a solid foundation for this sort of thing. But applying all of the interesting web APIs to desktop and mobile platforms, that’s not really something that Mozilla, Rust or browser developers can or should do anything about. They have somewhere between no and extremely limited clout in such spaces.
Yew (and comparable Rust frameworks) do however have a pretty slow compile time and with that a horrible debug-cycle. It's so bad that I in general opt for React-in-Yew for prototyping and only reimplement components with more complex state in Rust.
Not likely. The only thing that really matters to me is developer ergonomics. I've never seen a project struggle because it couldn't render a table with a 1,000 rows fast enough. I have seen many projects struggle because they hired a bunch of junior engineers who had difficulty writing clean, maintainable JavaScript.
Rust and WASM will definitely take on for doing things like WebGL. I can't imagine Rust becoming the de-facto solution for building UIs.
For starters, Rust: Rust is just too complex to be the most popular language when something like JavaScript exists which is faster and easier to get started with, and generally good enough. It has niche usage and will steadily grow, but it’s not going to take over the space any time soon, and probably never will. I say this as a Rust developer for seven years and a web developer for more than fifteen years.
Then the other part, discarding the DOM altogether: there are way too many pieces of functionality that the browser provides that currently cannot be implemented in web user space, for this to become mainstream any time soon. For example: correct scrolling, standard keyboard and mouse event handling, and accessibility. The idea that you would go from quite a few pieces of major functionality completely non-existent in browsers and specs (most of these issues aren’t even being talked about) to mastery of the space within five years is unreasonable.
For further shared abstractions, many web APIs are developed and continue to be developed. Other experiments like WASI exist. WebAssembly has scope to be a solid foundation for this sort of thing. But applying all of the interesting web APIs to desktop and mobile platforms, that’s not really something that Mozilla, Rust or browser developers can or should do anything about. They have somewhere between no and extremely limited clout in such spaces.