Easy Feedback uses UnityEngine.Input.GetKeyDown() to check for the F12 key for the time being. As far as I'm aware, calls to the old input system should be compatible with the new input system with the right project settings. If you'd like to use the new update system, you may modify the input check in FeedbackForm.cs starting at line 111. This guide should help you.
I'll look into supporting the new input system by default in a future release.