Hmm, well, I would charge him a minimal rent, as in paying the extra it will cost in food, heating etc. especially if his girlfriend is planning to stay there too part-time. You do not owe them a subsidy to move back in.
How about when he stays at her place? Is she with her parents? Or already living independently? How are they working that out financially-wise?
Just a month into university accommodation and wanting to come home? Why? You need to get to the bottom of this.
Does he just need more time to settle in?
As a solo mum of a son who also went to uni and lived there, I would not be pleased about this at all. No way I would be having him and his girlfriend living with me.
Visit? Half terms, during holidays? Of course. Always welcome.
But the big wide world is beckoning now. Scary yes. Always has been. But it's life.
I am a single parent, I don’t know if that helps.
Oh, it sure does from where I'm standing. We've always done it all alone. Now comes time for YOU.
You need to gently help him to become independent and pick up your own child-free life again.
The door is always open but not for moving in with anyone extra.
Good luck OP.