If the logic is compute heavy, Rust with Wasm can be a good approach. TypeScript on both ends is also a pragmatic choice. You can still have a boundary in the backend for lower level layers in Rust.

If the logic is merely about validation, then an IDL with codegen for TS and some backend language is probably better. There are also some more advanced languages targeting transpilation to both JS and a backend language such as Haxe, but they all have some trade-offs.