That sounds like it's getting a connection, then showing alerts it couldn't when there wasn't one. I know you don't have Data Saver on, but check your settings for anything that blocks a communication-type action when the phone is sleeping.
Also, see if changing your 'override do not disturb' settings helps. For Calendar, it's kind of convoluted getting there, but start in System Settings, and then Notifications. If you can't find its DND setting, post back.