It seems like private browsing is undetectable with DeviceActivityMonitor for two reasons:
- Specific web domains do not cause the monitoring threshold callback functions to fire, due to the privacy setting
- Safari is not able to be monitored as an app or a category. It doesn't appear in the FamilyActivityPicker, and it doesn't appear to belong to any Screen Time category when viewing Safari's information in Screen Time Settings
Is there any way to monitor device activity during private browsing? If not, that seems like a big problem for apps that allow parents to set device activity limits for their kids.