This project features a REST-API written in Rust and a multi-platform Frontend based on Flutter.
It is a puristic demonstration of the basic functionalities and code-styles of both languages. Both applications can be arbitrarily extended by e.g. authentication, user management, integration tests etc.
Although for this example it is certainly an overkill in complexity to choose rust as a backend language, there might be a various number of use cases why this decision could make lot of sense; e.g. if your BE is expecting lots of load and/or has to perform complex, asynchronous operations while maintaining memory safety and avoiding possible race condition is crucial.
You'll find further details in the READMEs inside the applications.