That's strange! DisplayFusion definitely shouldn't affect the functionality of the Win + Left/Right hotkeys in Windows. Is it possible that the window doesn't have focus? It would have to be the focused window for the hotkeys to work on it.
As an alternative, you can set a key combination on the "Move All Windows to Current Monitor" function on the DisplayFusion Settings > Functions tab. When you press that, it will move all open windows to the monitor that the mouse cursor is on.
What you could try is to give newly opened windows the focus. The trouble is you need to edit your registry to do this, so if you are comfortable with that and I must stress that ONLY change the DWORD I mentioned below then this is how to do that.
Press the Winkey + R to open a "Run" box and type REGEDIT into it then press Enter.
Your registry editor will open, click on HKEY_CURRENT_USER to expand the key.
Now click on Control Panel and then on Desktop.
In the right hand pane scroll down to ForegroundLockTimeout and click on it to open the edit box.
Click on Decimal then change the value from 20000 to 0.
Click OK and close the editor.
Reboot and any newly opened windows will have the focus.
See image below.
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