Put everything you don't want to manage into Rcs, RefCells, Boxes and the like, and you'll more or less feel like you're using a (verbose) GCed language (with a loss of performance and safety as a natural consequence).
> I enjoy Rust and have been writing it for quite some time. However, I feel like server side languages still have a long way to go. Client-side languages in comparison have been only growing better
The fact you call them "server-side language" is a strong bias. Not everything is a client/server app.