I’ve made these settings (already some time before posting):
exclude DAVx from the system’s automatic (power) management
allow Auto-start, secondary start from other apps, continue executing the app in background
I do not know, why it says “Power saving disabled: no” because there is no other settings that can be done.
For testing purposes, I set the sync intervall for the calendar to 120 min and for tasks to 15 min.
Result: ==> calendar is sync’ed, tasks are not