Modern JS frameworks pre-render the components on the server then they attach to them to "rehydrate" and add JS handlers on the client. They also allow mixing of purely-server-side components (essentially templates, no JS or hydration) and mostly-client-side components (that still pre-render on the server)

For Rust, Leptos (https://leptos.dev/) would be one choice that can do SSR+hydration (but not intermixed with server-side components, at least AFAIK not yet)