We managed to get Apple Classroom to work on iPads, but we couldn't get it to work as a teacher's device on the Mac. We are just trying a very simple 1 teacher device running Classroom and 2 student devices.
When starting Classroom on the Mac, Classroom doesn't detect that I've already logged into the Mac with my managed Apple ID. It doesn't detect any classes, and it doesn't detect my name (it asks for my name). I can't see a way to log into Classroom itself.
Also, I noticed there is no EDU profile installed on the Mac. This profile is present on our iPads. See screenshot below.
Devices are using the same Wifi and Bluetooth is ON. I've tried tethering off my phone's hotspot just to rule out the network - no difference.
Any assistance would be much appreciated!

