I was also facing a similar issue with my looped videos. With expo-video you have a couple options:

option 1:

• Set staysactiveinbackground = true, https://docs.expo.dev/versions/latest/sdk/video/#staysactiveinbackground
• It just means it will continue to play even in the background.
• The issue is that expo-video pauses the video upon entering background, which is not bad unless your supporting background audio and pip.

option 2

• Listen to AppState and when entering forground, start you video again.

    import { AppState } from "react-native";
  
    useEffect(AppState.addEventListener('change', (nextAppState) => {
        switch(nextAppState) {
            case 'active':
                // Video loop
                player.play() 
                break
            default:
                break
        }
    }).remove, [video.playbackTimerSyncedWithVideo])