I can't help but notice the difference in the situation with his last girlfriend where we knew her parents and would go out for dinner as one big happy family this jumped out at me! If this girl knows that you had such a close and comfortable relationship with his ex and her family, I imagine she feels a complete disappointment, and knows that you would rather things had worked out with his ex.
My inlaws were best friends with the parents of DH's ex fiancé, so naturally they all did lots together. I met him shortly after he had ended their relationship. His parents weren't unfriendly towards me but my goodness they had high expectations for my involvement with them, particularly MIL, when I just wanted to date their son! (we were early/mid 20s).
My widowed mother, with no money, status or connections, wasn't someone they could relate to (nor she them), and I'm sure they must have opined often between themselves how they wished it had worked out with his ex, and the lovely, affluent, confident, one big family get togethers could have continued. But their son ruined that for them by wanting something else. It's tough knowing you're a disappointment and tends to knock your confidence around the people to whom you are a disappointment.
I actually have a lot of sympathy for you OP, but I think this girl finds you all overwhelming. I'm much older and wiser now and I too am confident, relatively affluent, comfortable in my own skin, but I was that socially awkward girl around well to do, 'big characters' (although I would always at least say hello!). She's dating your son, not you, and you need to lower your expectations if you want things to improve.
I struggled for years with my inlaws (MIL). Actually went NC for a while after yet another load of criticism reached me via DH, that I was difficult, didn't make them feel welcome, blah blah. It wasn't true and was so unfair, I just couldn't give them the DIL experience they hoped for and expected, and until they could respect that I was going to protect myself. Things evolved and we reached a level of understanding and mutual respect that continues to this day - 38 years on!
I would advise you to step back and stop trying so hard. Never criticise her to your son - he will get defensive and it will become a "them and us" situation. Stop asking her lots of direct questions, just make observations about things, eg TV -"I've been watching the Australian Traitors and much prefer our version. It's not the same without Claudia, her knitwear is just fabulous - I wonder if she chooses it herself?" Pets - "I saw a man who looked just like his dog yesterday. I think it's funny that owners eventually start to look like their dogs - I wonder why that is?" You get the gist. And I don't suggest you try to engineer one to one time with the gf - that will terrify her.
Fact is it's far more likely to run its natural course if you leave them be, than if you try too hard. The most important thing is is she good to your son? Does she champion him, support him, share his dreams and goals? If so, the rest will come over time.