YouTube is restricting the picture-in-picture feature to only those who are YouTube Premium users. The PiP feature got native support in iOS 14 which started rolling out shortly after Apple’s September 15 event.
Many apps like Apple TV, Firefox, Google Chrome, and all the videos that play on Safari support PiP, except YouTube videos of course. The ability to play videos in the background and PiP are some of the perks YouTube Premium users already have on Android.
Currently, you can play any YouTube video in PiP via Safari on an iPad without needing a premium subscription. More apps will include support for this feature in the coming weeks.