Real-world Rust programs don't implement linked lists. There's LinkedList in libstd if you really wanted one, but in modern architectures cache locality is so important that almost always some other data structure is a better choice. Rust's standard library and crates.io have plenty of containers to choose from.
Linked list is popular because it's a CS101 topic, and because C is so barren. When you don't have any containers in stdlib, dependency management is hell, and due to lack of generics any 3rd party implementation will be either inefficient or full of macros, only then low-effort hand-rolled linked list seems like a sensible choice.