from looking at the documentation here https://docs.moodle.org/dev/openbadges you'll have to do two things
1. Write something (extension/component) to display the badges from your open backpack in the drawer
2. This is optional - write something similar to the Mahara integration that displays the badges that are in Moodle and not in the open backpack in the drawer.
I'm curious to how you are awarding badges - In Moodle you can award a badge for the completion of a course. The Adapt module is an activity that can go towards course completion, but until you complete the activity and the course the user will not be able to see the badge awarded for that specific Adapt module until the course completes.