I assume there should be some way to list out the spaces based on which permission groups they are in, yes? Could someone please help me with this request?
I don't think there is a single API call for that.
You can get the users permission for space/place using the permission entities as described here: Jive REST Rest API v3.9 → Entitlement entity
However, you will need to retrieve this on a per space basis.
Retrieving data ...