I have integrated the new Unity Input system, using this Video Keyboard and Joystick Controls in Unity 2019! (New Input System Tutorial) - YouTube.
As I wanted to implement UI I did not manage to get the buttons to be interactible. I have the feeling that the new input system is not set up properly to work with the Unity UI.
As I inspected the EventSystem GameObject, It displayed a warning that it is not set up to work with the new Input System and prompted me to fix it. I clicked on that and a new component was added with the InputActionsAsset assigned. 
This is what the Error looked like.
It did not work after that still. And adding the UI part of the created default Input Asset to my other InputActionAsset, which already works in game did not do the trick as well. Now it looks like this 
I would heavily appreciate any help on this topic.
I have recently run into this. It does work - try it in an empty project.
The problem is likely that you have more than one PlayerInput script active while the UI is active, and one of those is grabbing the primary (even if it’s the only) user’s controls.
You can likely solve this by ensuing you set the “UI Input Module” in your PlayerInput to your EventSystem object (it will pick up the correct script), as well as ensuring that you only have one PlayerInput active at any one time.
I ran into this problem in an empty scene with no input desired. Yes, you have to Add a PlayerInput component and then link the EventSystem to it for this error to go away. Alternatively, I think you can just disable the raycasting on your Canvas and Images.