My GF broke things off, immediately slept with someone else and now wants to get back together.

My 35M girlfriend 30F of 9 years broke things off because she was burnt out. I understood her reasons and since then have seriously work on myself and have made massive changes to who I am as a person. I did these things for me because I realized there were aspects about who I was that needed to change.

About 2-3 days after we broke up she slept with a coworker. This went on for several weeks to my knowledge. We live together still and I have been traveling for work and come back on weekends. For the last 3-4 weekends we have been “working on things” and have what seems like a new found love for each other. The sex is incredible and we both seem genuinely happy with the new “relationship” whatever that is. I am not putting a label on anything and just enjoying whatever this is at the moment. I’ve started talking to other girls myself but haven’t perused anything with them.

I believe she is still talking with this other guy, and has a work trip scheduled in a few weeks to the same city that he lives in.

I’m wondering if anyone has advice on how to navigate this? It feels like cheating to me and am wondering if this is something that can be forgiven?