Typescript has been used to write pretty much anything, from websites to their backend code, to command-line tools, to machine learning, chances are that if the problem exists, someone has written a solution in typescript.
Typescript is a very easy language to write (provided you don't go too deep into the type system, which you shouldn't really have to unless you're developing a library), which is why it is everywhere. Why spend lots of time developing in more complicated languages like Rust or C++ when you can do it quickly without having to spend painful hours dealing with manual memory.
Dart, like Typescript, is a pretty easy language to write, and my argument is that if you want to use Typescript, you might be better off using Dart instead. For most of the scenarios that I'll look at, you should really use a lower level language, like the two mentioned above, however, when has a best practise ever stopped a developer from doing something.
A brief introduction to Dart
Dart is a general purpose programming language supported by Google. Originally concieved as "Typescript but better", it shares a great deal of syntax with Typescript, which should make it a relatively easy language to pick up and understand for most people. It is a versatile language that can be compiled to number of targets (including javascript but why would you actually want to do that)