Your girlfriend needs to know you are married.

You are both attached. She has a boyfriend and you are married. Not a good idea

You separated a month ago and already found woman of your dreams. Not realistic

She doesn’t claim you on social media because it’s an affair. People won’t claim those anywhere

Even if she leaves this boyfriend for you, she’ll leave you for a new man just the same.

Your wife is cheated but now you are with another cheater. Look into it. Why are you attracted to dishonest cheating women