beorg doesn't have a serverside component so can't update the counter unless it is run. beorg does request that iOS run it in the background to refresh tasks and update the counter, but whilst this may happen several times in a day there will still be a delay between a task becoming due/overdue and the badge updating. The message you receive from beorg is called a local notification and no beorg code runs when you see this appear on your screen.
Ian Charters
I get notifications for timed tasks on time, as expected, but the icon doesn't display a a counter until after the app is opened. This behaviour is the same on my iPhone & iPad.
iPad: beorg 3.10.1(227), iPadOS 14.5.1
iPhone: beorg 3.10.1(227), iOS14.5.1
Is this expected behaviour?