I know what SSR is and you can do it[1] in Rust, where you write type-safe, compiled Rust code and send HTML/CSS/WASM to the browser. SSR was originally developed in things like Perl and PHP -- there's nothing language-specific about it.

> Besides being less efficient than JS at manipulating the DOM

Some applications manipulate DOM a lot (and WASM isn't slow enough for a well-written app to be noticeably slower to a user) and some applications do a lot of processing before changing the client. WASM will be dramatically faster at the latter.

1. https://wasmedge.org/book/en/write_wasm/rust/ssr.html