22 July 2021
UPDATE (July 12th, 2022):
YouTube's Picture-in-picture (PiP mode) for iPhone and iPad is finally getting a wide release. It will be available for everyone in the United States but if they are not Premium users, they cannot use it for non-music content. Users from outside America will have access to PiP mode only if they are Premium subscribers and they will be able to use it for music content as well.
They will also need to ensure that their devices are running at least iOS 15 or iPadOS 15.
Original (June 21st, 2021)
YouTube is finally rolling out native picture-in-picture (PiP) mode support for iOS and iPadOS users. The mode is available on Android devices since 2018 but it was under testing for iOS counterparts since last year. It seems to be satisfied with the testing results as it is now working on expanding the feature to all users.
The picture-in-picture aka PiP mode allows users to watch video content while using some other app on the device at the same time. It improves multitasking capabilities as users are not restricted to watching videos anymore. It can specifically be helpful when you are taking notes or texting someone while watching a video.
The YouTube PiP mode on iOS will work on both iPhones and iPad running at least iOS 14. It is currently limited to YouTube Premium subscribers but will soon be expanded to free users. Another important thing to note is that one needs to be in the United States to get this feature. This seems to be a part of the gradual release and should expand to other regions sooner than later.
If you are unable to access YouTube PiP mode through the app, you can still use it via the web browser. Just sign in using the Google account that you used to get the Premium membership. Next, play any video in the full-screen mode and then tap the PiP icon in the top left corner.