When navigating with the mouse, the modal blocks much of the view and blocks the global context. I cannot click "under" the modal. Similarly, I should not be able to trigger "global" shortcuts that have an effect outside of the modal when a modal is open.

We should modify TLP to trigger some sort of custom event when any modal is open. "Keyboard navigation" would listen to this event and disable the shortcuts.
The modal, when closed, would trigger another custom event and "Keyboard navigation" would listen to this event and enable back the shortcuts.
This should replace the actual system of events triggered on the modal itself, which should be replaced by a callback system. This refactoring however can be moved out of the scope of this story.