Hi,
i have exactly the same issue. My daughter has her own iPhone and I have setup her Apple Watch with this device. I can manually enable Schooltime directly on the watch, but cannot monitor or setup a schedule on my or her iPhone. The Problem is, that schooltime is somewhere hidden in the watch app, tricky to find. And if you don't want to use Family Setup (or cannot, because your carrier is not supporting this feature), it's not appearing.
The solution could be very simple and much more logical anyhow: Please integrate the Schooltime setup in screentime. Screentime is a tool many parents already use for their kids devices (iPad / Iphone) and this would be the best place to integrate Schooltime as well. Logically the two features belong together. By that everyone can control and setup school time, even without family setup.
Regards