I can confirm meeting the same issue, while using video background in OpenLP 3.1.1. Here is how you can check the bug:
1) Theme background type is set as Video with 2:00 duration;
2) After church finishes singing I press ESC button and OpenLP Live window switches to Show Desktop mode;
3) Though no songs are presented the Video timer in the bottom of the Live window keeps going;
4) After 2:00 video finishes it goes on a new loop, while OpenLP starts presenting the video background without any verses;
5) OpenLP has the same issue if I switch Live into Go to Black mode. After 2:00 and new video loop the Black screen overflows all other windows including PowerPoint 2021 and BibleShow 5 in presentation modes.
I checked all possible settings trying to fix the bug myself, however all my attempts failed. Please consider fixing the bug in the following updates.