You could try removing one of the plugs and re-adding it, it may goose the plug. But there are other posts about the Plug badge not showing up for some.
You should (are supposed to) get the Digital badges in the app regardless of when purchased, but the gamification process behind this is all wonky.
You used to get an “I backed boarder” for pre-orders on the digital badge, and stickers.
If a connectable IoT device, a badge should show. There are some discrepancies at the moment… i.e. the Safe.