I’m using Drafts in macOS, iOS, iPadOS and WatchOS. Latest versions on each. The badge icon shows the number of items in my Inbox on everything but the Mac. But … after I click on the Drafts icon in my dock, then the badge shows the number of items in my inbox.
I have allowed Notifications for Drafts in settings. And in Drafts settings I’ve clicked Launch at Login. Not sure why it’s holding back the badge until I click on the app.