Apple's support article "Use Quick Start to transfer data to a new iPhone or iPad" has this verbiage at the bottom:  "If your new device is enrolled in Apple School Manager or Apple Business Manager, you can't use Quick Start to transfer data from your current device."  The article was recently updated, so appears iOS 16 has the same limitation.

Apple's support article "Use Quick Start to transfer data to a new iPhone or iPad" has this verbiage at the bottom: "If your new device is enrolled in Apple School Manager or Apple Business Manager, you can't use Quick Start to transfer data from your current device." https://support.apple.com/en-us/HT210216 The article was recently updated, so appears iOS 16 has the same limitation.