You don't have to reimplement them yourself, they already come provided with the same components as on the web, like buttons, forms etc (and there are also custom UI frameworks like forui which clones shadcn/UI if you're familiar with that). The point being, Flutter apps can run much smoother precisely because they reimplement everything rather than dealing with the legacies of HTML and CSS. Since your UI seems fairly simple to make in any UI framework, you could take a look at Flutter as well.

I do so with Rust also with the package flutter_rust_bridge which works great, I'm working on a mobile app that also simultaneously works on web and desktop when I tested it, even all the Rust parts.