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:
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.
I'd also like to plug ReVanced. You do have to provide your own copy of the YouTube APK (easily downloadable from APKMirror), but it allows you to install multiple patches into the app, including Return YouTube Dislike, SponsorBlock, and other stuff. It allows background play and blocks ads, too. (You can see the list of available patches here.)
Problem with that is that I want to use my subscriptions but using that app might get my user potentially banned and I do not want my google account banned.
I've used ReVanced every day for over a year now and nothing has ever happened to my Google Account. I also used regular Vanced for at least two years before that, never had any issues.
You could create a burner account to be on the safe side. I believe there is a way to export the channels you've subscribed to and I port them to a new account. Haven't tried that myself though yet.
The problem I have with ReVanced is that it sometimes doesn't register videos as watched or doesn't save the watch progress. It happens pretty randomly too, one week everything works correctly then the other week nothing I watch gets saved
Huh. The only time I had that issue was when my adblocker app was blocking a specific domain that the YouTube app needed unblocked to save watch history. I unblocked the domain, and I don't think I've had that problem since. I had to unblock s.youtube.com/api/stats/watchtime, though the internet says it's changed to youtube.com/api/stats/watchtime in more recent years.
Ah, sorry, I guess I dont understand the difference between watch later and a playlist. Since you metioned a playlist I assumed you were talking about saving the actual file to watch later.
And for iOS I can recommend uYouPlus (https://github.com/qnblackcat/uYouPlus). The cheapest way to sideload it is using AltStore. But there are other services which offer sideloading on device, these don’t require a computer.
You geht downloads and subs with NewPipe, too.
But it boils down to preference. And I prefere a open source app to begin with instead of patching something.