GET /api/oauth2/v2/campaigns/{campaign_id}/members
Is probably what you’re looking for. This should return anything from an active patron to a former patron to a follower. Just make sure you request the right fields.
Alternatively, if you do it through the member’s tokens, and store the tokens, it’s just a matter of refreshing them if needed and gathering the updated data. My app does this rather than the above because I need to check for current patron status to ensure rewards are granted fairly to those who should have them.