After years of dealing with addiction and all that goes with it, we adapt and it becomes our "norm", however dysfunctional. We get used to it and know how to act and respond..and wisely we learn to let go.
You are in a new, healthy relationship and that may feel strange for a while. It's not what you are accustomed to, it IS what you deserve and I hope things go well for you.
My suggestion is to keep moving forward, don't look back, the past is not worth repeating. Take the lessons with you as you grow in a healthy relationship.
Whether this new relationship pans out or not, you are wiser for having seen and recalling how relationships are supposed to be, each bringing something special and sharing together while each maintains their own identity and is not dependent on the other.
Sick attracts sick, healthy attracts healthy. You are doing well to see the difference.