Give the language tour a quick look: https://dart.dev/guides/language/language-tour
I've been using Dart since the start (~8 years ago), and follow language development very closely.
Let me know if you have any more questions.
Frontend - Flutter for the UI (Android, iOS and Web) Backend REST Services - Pure Dart or Aqueduct.io for more complex apps Scripting on my PC Command Line Interfaces for different Tools Advent of Code solutions Blockchain stuff Chat bots ... much more
So why do I like Dart?
The default libraries are amazing - dart:convert, dart:io and more. The asynchronous language features like async, Future and Streams are the best ones I found in a language until now. The Dart and especially Flutter docs (just look at the animation curves section) as well as the official YouTube videos do a great job of teaching different subjects. The combination of dynamic and statically typed objects and variables works really well in most cases. The List and Map operators are really good and easy to use. Package management with pub works and is fast.
Disadvantages
The Ecosystem for non-mobile apps needs more libs.
Conclusion
Try Flutter and see if you like working with Dart, it's very easy to pick up.
Definitely gonna try flutter for web though--im ready to say goodbye to React completely.
I have spoken to people who have used it for backend code, though that is rare.
In the latest release they added support for creating standalone binaries. I haven't tried it but it sounds promising.
There is a good package manager and a decent selection of libraries. I haven't tried it out lately though.
I like a lot of what Flutter offers for cross-platform development, but it's hard for me to justify the cost of learning a separate language just for one tool, versus (for example) React Native which uses a multipurpose language with a massive ecosystem of existing libraries and tooling.