7.1 nougat – Dialogs of Apps don’t show

I am running stock Android 7.1.1 on a Moto Z Play.

Recently I noticed that popup dialogs from apps running in the background or also in the foreground don’t show automatically any more.

So, e.g. I have the apps Reminder with Alarm and Automate.

“Reminder with Alarm” has an option to show reminders as full-screen alarms with sound and Automate allows me to create widgets that, when pressed, should show a popup with a selection.

Both apps have the “Draw over other apps” permission enabled.

What happens instead of the popups being shown is that I only get a notification and when I press that notification the popup is shown.

I tried reinstalling these apps and also all other apps that reasonably could influence that behaviour. How can I further debug what is prohibiting those popups being shown?