The following patch should fix this issue. Could you please try it out?

Index: NoesisView.cs
===================================================================
--- NoesisView.cs	(revision 16730)
+++ NoesisView.cs	(working copy)
@@ -1319,10 +1319,6 @@
     {
       #if ENABLE_LEGACY_INPUT_MANAGER
         Vector3 mousePosition = UnityEngine.Input.mousePosition;
-      #else
-        Vector3 mousePosition = UnityEngine.InputSystem.Mouse.current.position.ReadValue();
-      #endif
-
         Vector3 p = Display.RelativeMouseAt(mousePosition);
 
         if (p == Vector3.zero)
@@ -1332,6 +1328,11 @@
 
         _activeDisplay = (int)p.z;
         return p;
+      #else
+        Vector3 mousePosition = UnityEngine.InputSystem.Mouse.current.position.ReadValue();
+        _activeDisplay = UnityEngine.InputSystem.Mouse.current.displayIndex.value;
+        return mousePosition;
+      #endif
     }
 
     private void UpdateMouse()

The implementation of MousePosition should be like this:

    private Vector3 MousePosition()
    {
      #if ENABLE_LEGACY_INPUT_MANAGER
        Vector3 mousePosition = UnityEngine.Input.mousePosition;
        Vector3 p = Display.RelativeMouseAt(mousePosition);

        if (p == Vector3.zero)
        {
            return mousePosition;
        }

        _activeDisplay = (int)p.z;
        return p;
      #else
        Vector3 mousePosition = UnityEngine.InputSystem.Mouse.current.position.ReadValue();
        _activeDisplay = UnityEngine.InputSystem.Mouse.current.displayIndex.value;
        return mousePosition;
      #endif
    }

Hi and sorry for the late feedback.

We did some first tests and it looks promising. But so far it only seems to work in standalone builds which makes it a bit tricky to use for development.

The mouse z is the index of the screen and that doesn't work in the editor.

If you open a second game screen in Unity and set that one to Display 2 the mouse display index (z) will still return Display 1 the entire time.

This would be probably helpful to be added or used to get the right one in editor mode: https://docs.unity3d.com/6000.3/Documentation/ScriptReference/Display-activeEditorGameViewTarget.html

The main issue we have in the editor is that OnGUI is not invoked on secondary displays. The proper solution would be to deprecate OnGUI entirely. This is something we’re considering for Noesis 4.0, but I can provide you with a preview in 3.2 (disabled by default) so you can try it out.