There's fundamental difference between C# standard library and Rust standard library.
C# includes in it's standard library lots of things which may be nice for the developers to have.
Rust tries to include only things which have to be in the standard library, lack of which may fragment Rust community (imagine standard library without String) or which are not possible to implement in a stable Rust (like Fn/FnMut/FnOnce traits).
Everything else belongs to the “third-party” crates.
P.S. It would have been really nice for novices if there would have been a nice set of crates which can, together, be considered a replacement for C#/Java/Python python SDK. Set of well-developed crates which solve common needs and are considered “good enough” today. There would be no need to keep everything in that list supported “forever” (like the stuff in standard library) but at least it would be a place where you can go and find out that crate Foo is no longer supported and Bar is it's incompatible replacement. Like “RLS is obsolete, try rust-analyzer instead” (something which makes quite a few total newbies make the wrong choice).
FWIW, this set of crates does exist. It's just that they aren't formally listed anywhere or endorsed, and the set will change over time. Often you just need to go to crates.io, type a keyword into search, and look for the most popular result.
serde - general serialization framework
serde_json - JSON
reqwest - HTTP client
ring - crypto
byteorder - utility for handling little/big endian numbers and byte streams
anyhow - error handling in top-level applications where you care more about things like backtraces and what caused what
thiserror - error handling in libraries when you want to define your own fine-grained custom error types
clap and/or structopt - for command-line argument parsing