I will need to add something that maybe helps figure out what's going on:
I've created a script that uses the API to create a group. That works fine now (yay I'm doing it the right way). The weird thing is that after creating a group in a course via this method, now all the groups that the admin couldn't see before are showing up. It's like creating a group "the right way" somehow "enabled" all the groups that were created in the wrong way.
I've double-tested this with a second group in a second course that had the same issue, checking right before if I could see the groups with the admin account (I couldn't), then creating a new group in that course via the API, then checking again and then those groups became visible. Very weird!
I would still like to understand what's going on if at all possible, I'm sure there has to be some sort of explanation.