I am currently learning Dart and Flutter in my free time (using it for a hobby project) and so far, I haven't seen any real use case for Dart alone.

To me, Dart is Flutter. I don't think the Dart team have tried to make their language stand out and show its usage outside Flutter. I mean I enjoy the language a lot, it's really faschinating using it and reading the docs but it doesn't provide any value alone sadly.

I am well aware of all the fullstack frameworks poping up every second, but I think if the team created such framework in the language then that would definitely prove it's capabilities and maybe attract more people.

When I think about it, Ruby and Rails is in a similar situation. The only reason people are learning Ruby is because Rails, but to my understanding (forgot the source) but the team behind Ruby is well aware of this and is trying to prove Ruby's value outside Rails.