Unfortunately, the bagde icon (number of due tasks) in Omnifocus 3 will not be updated overnight.
Although the app runs in the background, it must first be opened to update the icon.
On the other hand, Applewatch works without opening the app.
I also tried to create a new group in the “push settings” - unfortunately without success.
I simply subscribed to a daily newsletter (https://nl.faz.net) on the omnifocus email address - obviously the arrival of the email triggers the counter. I have not found another solution - but I’m satisfied with it.