You had only been seeing each other for a month and weren’t actually girlfriend/boyfriend so I don’t think it can really be considered a breakup so much as just not spending as much time together, and the “break” part of it is just putting a hold on the expectation of building a relationship. I would just back off for a bit, not try to hang out unless he asks you to, maybe not message him every day, but I would definitely still check in on him once in a while just to ask how he is and how he’s feeling, because that’ll show him that you care about him. Keep the lines of communication open.