I've used most available services, but discontinued one after another along with promises that a better user experience will be provided with reduced content and removed functionality with the slight price hike. YouTube was my first and last video service I paid for, only Spotify remains on the borderline.
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:
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.
On Android just use Brave browser and turn on the setting to allow tabs to play media in the background. Opera does the same thing.
Not sure what iOS options there are.