Thanks)
It's not really hard when you work with Unity.
The hard part is to make it work with UI. And I didn't 😅
I believe by default if you're using the new input system things such as buttons should automatically work
They should. But you need to setup navigation between buttons and set a button to be selected by default. Then you can use stick to navigate.
Without that you can't navigate until you click with mouse on any of the buttons. So UI needs additional setup. But basically yeah. It's almost ready.
