“Magic links” are a different approach. Instead of a single, long-lived password, the web app generates a new, unique secret code every time you want to login. The web app then sends you an email or an SMS with a link to login. This link contains this unique secret code: your short-lived shared secret.
On the Rust side of things, just TCP is implemented in the Rust Core. The current web frameworks (actix and rocket) are implementing everything up until HTTP though. So you don’t need to care where this is coming from.
If you want to use pure HTTP calls without any larger framework, you can install “crates” (equivalent to npm packages in the Node world) which implement the HTTP protocol (like hyper and tiny_http).
Actix web is a small, pragmatic, and extremely fast rust web framework.