According to the Daring Fireball website, the Apple Studio Display runs the full version of iOS 15.4. In System Report, Graphics Card/Monitor tab, you can see the software version of Studio Display, Version 15.4 (Build 19E241).
This version number is the same as iOS 15.4 and iPad OS 15.4, which means that Studio Display runs the full version of iOS. Apple Studio Display is equipped with the A13 Bionic chip, which is the same chip as the iPhone 11 series, the 2020 iPhone SE, and the ninth-generation iPad. The Studio Display supports a 12MP ultra-wide-angle front-facing camera, Center Stage support, and a 6-speaker system that supports spatial audio.
Previously, it was speculated that the Studio Display was running a special version of iOS, similar to the HomePod mini running a special version of tvOS. However, it is now certain that it is the full version of iOS 15.4.
In the first reviews of the Studio Display, many reviewers found the camera to be unbelievably bad. Subsequently, an Apple spokesperson said that in the future, a software upgrade will be used to solve the problem that the front camera does not perform as expected.
