Sorry for that, I've clarified in the post.
You need to be signed in to google to join the group. If so then you can click on the app links and install in on the android device.
The account you use to join the group must be the same on the target android device.
Unfortunately google has these draconian requirements for personal developer accounts, where they require "at least 12 testers to be opted-in for at least 14 days" during this "Closed Testing" phase, just to unblock production access.
APK sideloads do not count as far as I know.
I understand the motivation (reducing abuse and malware), but it does make things harder for small personal developers. Business accounts don’t have this requirement, so I may look into that.