I do not use Jamf School, but as far as I am aware the only way to issue OS updates is with MDM commands. Configuration Profiles just set the requirements for OS updates (i.e. how long until the mac sees the update after release and such). As of this point Jamf has made no "policy" method to automate pushing the OS update command, you must manually send it each time. However, users can be offered the option to defer.
I have not used superman, but to my understanding you need to push the install macos.app and then run the erase all contents script with a flag to not erase all contents. This method provides no warning for the user once the script starts, the device will just reboot when its ready.
We exclusively use MDM/DMM commands to issue OS updates. The OS update workflow is painful due to Apples poor design, and Jamf refusing to offer any automation in issuing the command, but it is what it is. We also have a Jamf Helper policy run daily on devices. IF the device has pending updates, it will notify the user and guide them through installing. IF they have no updates, it just exits. We empower our end users to install OS updates when possible, and enforce them a week or so after release. We usually see around 75-80% patching compliance just from end user interaction with all the notifications we give people and are usually over 90% by the end of two weeks (we force the update the 2nd week).
