Hi @Chris Barth
I searched a lot but didn't find a way to disable copy/paste in Edge kiosk mode. The only related feature in kiosk mode is Read only address bar (policy). If you disable this policy KioskAddressBarEditingEnabled, it can prevent users from pasting/editing in the address bar.
As the document says Apps that run in kiosk mode cannot use copy and paste, but copy/paste is still usable in Edge kiosk mode user experience, I suggest that you can provide feedback to Edge team about this issue. You can press Alt+Shift+I in Edge to send feedback. Edge team will check the feedbacks and improve the product continuously. Thanks for your understanding.
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Regards,
Yu Zhou