[Task] Move thread intercept handling to unified input thread #13438
Open
Description
Followup to #13398
Instead of the overlays managing intercepts, this should be handled by the overlay input manager. Some extra plumbing is required however:
- Track all 3 input masks for all overlays
- Get rid of raw calls to run_input_loop (media list dialog)
- Handle intercepts tracking in the overlay manager. The state is pushed forward from the first overlay and released at the very end when there are no items remaining.