The short answer to your question is simply no, it's not possible to install Visual Studio on Xbox One.
The Xbox One developer mode is isolated, and it can't install Win32 applications like Visual Studio (Though, it's probably possible to install console applications or just simple apps that runs on background, since the Xbox One OS is based on Windows).
The solution
If you have a computer that have Windows or macOS (Maybe Linux with Wine), you can install Visual Studio 2019 for free and install these components :
- The UWP Devkit
- The C++ or C# module (Or both if you combine different languages)
And that's it. Your app will be compatible with Xbox One and Windows because it's universal.
But, don't forget to read that to make sure your application will work as expected on Xbox One: UWP features not supported on Xbox
If you need more details, you can see the Getting started with UWP app development on Xbox One