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As it were, it's being used as such to implement a Tink-compatible Rust library as part of Google's Project Oak.
The main difference between those two languages, I think you should look at, is power of type system. A good type system allows to encode various invariants checked at compile time, help with interoperability, and even improve performance a bit (e.g. by eliminating runtime-checks). In this regard Rust is far, far ahead of Go in my opinion and continues to improve in this regard (e.g. soon we will have const generics). For example, in RustCrypto we have trait crates which contain "interfaces" of several algorithm types. Almost all algorithm implementations in this org (and some third-party implementations) are implemented in terms of those traits, which means you can easily swap algorithms with each other and combine them like Lego blocks, without diving deep into source code. This property is especially important if you want to support less common algorithms (e.g. regional standards or newly developed algorithms).
Of course, Rust cryptographic ecosystem also contains "traditional" libraries as well, such as wrappers around OpenSLL/libsodium, OS crypto providers, and notably ring. To add a bit of promotion: ring heavily borrows BoringSSL code (Google's fork of OpenSSL), intentionally restricts number of supported algorithms, and is used by rustls, which has noticeably outperformed OpenSSL.