Having the same issue, and I can confirm it's working fine (seamless animated looping) on a Widows 10 machine with OpenLP 3.0.2 , whereas a different machine with Windows 11 and OpenLP 3.1.0rc4 displays a split-second (multiple frames-worth) full-screen black when a video background gets to the end before it loops back to the beginning. Very distracting when the video is the background for a song.
I tried what "oykleppe"#p25446 suggested, trying various File caching values in VLC's preferences, from 0 to 300 to 1000 to 4000ms, and they had no effect on the problem from within OpenLP. Note that the issue doesn't appear when viewing the animated background video directly in VLC, only within OpenLP (which of course does use VLC in the background).
I bought a new machine for our church and upgraded OpenLP to 3.1.0, not realizing 3.0.2 already supported videos (up to this point I was doing animated backgrounds as animted GIFs, having converted them earlier). Using real videos rather than animated GIF equivalents is much nicer, but I'll need to stick with the animated GIFs until this gets resolved, or revert back to 3.0.2.