As you said, this works for him. Why would he change it? It seems he feels guilty about the divorce and is keeping things as unchanged for his kids as he can. He’s also trying to make up for it by being more like a buddy than a parent. I’m sure he genuinely loves his kids. I’m reasonably sure he also loves you. But on some level, he’s not coming to grips with his new reality and isn’t able to help the kids make the adjustment either. Meanwhile, you participate in the situation by paying all the bills and accepting the way he is structuring his life.
I’m not going to tell you to leave him. I don’t know enough about him. I do suggest you make an appointment with a therapist who specializes in divorced and restructured families. Go by yourself a few times to lay the groundwork. Then invite your partner to join you. The two of you need to work together to figure out the role you will have in the children’s lives and how he can be a supportive father while they adjust to the entire situation. Ideally, you will also develop at least a courteous and respectful relationship with his ex. After all, you will be co-parenting the children as they move back and forth between your homes. If your partner won’t join you in the project, you’ll have the information you need to decide what you need to do.
I wish you well.