Don't get me wrong, a HTML5 radio button is a beautiful thing, and sometimes React is a hammer and everything is a nail.
However, I think something that OP doesn't mention super explicitly in their post is the codebase they are working on is probably a React codebase. React is a great abstraction for building UIs. I've built a ton of them and the complexity only needs to go above a certain degree until you need a way more descriptive way of explaining your UI based upon other state, instead of trying to wire a load of DOM elements together.
If you are already using the React ecosystem, for things like form validation (again, possible with HTML5 but as soon as the complexity cranks or you can't use the server - you probably need a library), then using something like Radix is a great choice, OP even mentions how although it's not technically a visible radio button that is shipped to the DOM, it acts like one for a11y reasons, and this is due in part because it's very, very easy to write inaccessible HTML. And ShadCN is pre-made components on top of that, and they all work pretty well together.
Nothing is perfect, but even in my "old man yells at cloud" era, I personally don't think this one is worth yelling at the cloud for.