I can't find information of what usecases both languages fulfill.
That's funny. For years, you couldn't throw a rock without hitting a bunch of people comparing these languages. Maybe everyone stopped doing that for some reason.
Go is designed primarily for network-facing daemons. Google makes a shitload of those and assigns that kind of work to new hires to keep them busy. It's become quite popular for web service backends, and also for container-related software used for managing virtual servers, I guess because the same people are writing those.
Rust is designed as an alternative to C and C++ for real time or "bare metal" code, but without the constant danger of crashes or RCE exploits. Its first use in production was in Firefox. Now it's being used in Android and Windows, and graphics drivers in Asahi Linux. It has a reputation for being "obsessed" with safety.