Based on the screenshot I assume that you used youtube premium lite (what ever this was…) on your smartphone. Therefore, here the obligatory recommendation for NewPipe. Quasi Youtube Premium as apk. It has all the features you need:
no ads
you can close the app and your videos keep running in the background
you can turn off the screen and your videos will continue to run in the background
There is also the fork NewPipe x SponsorBlock (link to repository) which integrates SponsorBlock into the app. (duh…) This will also skip the creator’s ad blocks in the video.