[moltonel3x]

You'd need a few different ones, just like curl itself uses a lot of 3rd-party libraries to provide its full feature set.

Some likely first choices would be hyper (http client/server), rustls (encryption), tokio (async scheduling). The Rust ecosystem is quite rich in protocols and codecs, it shouldn't be too hard to find most (all ?) of the crates you need, but there's still work needed to bring them together into one curl-like tool.

Note that Rust crates tend to be more focused than what you're used to in C, made to be composed together instead of used as a one-stop-lib. So your dependency tree would look much bigger than curl's.