OP I am kind of in your GF’s position.
I have never really found it easy to make friends, I get on with people but for one reason or another people never approach me first it’s always the other way round.
My partner on the other hand has a fairly decent social circle, although he downplays it in front of me I think because he knows that it’s not the same for me.
But in general if there is anything social being arranged he is the one who is invited. We know the same people, but they always communicate with him, and I’m never part of that plan. And although he’ll tell me that I’m obviously invited, we both know that they expect him to bring me because we’re together, but that I’m not actively invited, iyswim.
And so I step back for his benefit.
Unlike your GF though I don’t expect him not to go, but if he gets invited somewhere I automatically assume that it’s him being invited and not us.
It doesn’t actually bother me that much. He’s come home on occasion and said “oh x has said that we definitely need to go together next time, they really want to see you,” so I suggest meeting up or doing something and suddenly they’re too busy, and then he gets an invite somewhere when they know I’m not available.
I’m not a victim, people are free to make their decisions about being a part of a friendship group, and I don’t expect my partner to pay the price for that. If I did go I know that we’d all get on, but I don’t want people to feel awkward if I’m there when they know that they hadn’t even thought that I should be included.