You've gotten a lot of good things to think about in many posts. I have a daughter this same age (a bit older -- nearly 12.6 if you want to put it that way) and she also is going into seventh grade in the fall. So I know lots of girls this age and know some pretty well, besides my own kid.
I would add to the other advice:
Do you have her doing any kind of organized class, camp, one-time workshop, sport -- anything like that this summer? You don't mention it. I am a fan of one-on-one time with kids who are already her friends but it sounds as if she could really use something like a focused, organized, directed activity for some of the summer. She would meet new kids who are not already known to her; she would be engaged in an activity (physical like sport or camp, or mental like an age-appropriate kids' class in art, drama, computer graphics, whatever interests her). That would help her get outside her own head and her own emotions; it's hard to stay down and silent if you are doing an activity you like. It is not too late to hunt down some kind of activity -- and be sure to get her to help choose so she WANTS to go. You might have to prompt her a bit but please try. Do not, not, not tell her "this is because you don't want to go anywhere or see your friends"! That will sour her on doing anything. But DO see that she goes every day or every class, and don't let her bail out with "It's too hot, it's not what I expected" etc. -- tell her it's just for the week or just X classes long, not forever. And during the school year, is she in Girl Scouts (not in a troop of all classmates/friends) or sports (not with classmates) or a church youth group or any organization/class where she has friends who have nothing to do with her school or neighborhood friends? It's good for kids to have an outlet where they make other friends who are not part of the school or neighborhood groups.
Definitely do not throw some party for her. Having a bunch of kids over, even kids who were or are her friends, could be overwhelming for her. And it smacks of trying too hard. Unless she, herself, wants to have a party or sleepover, do not push this kind of group interaction right now.
Someone suggested going away with her for a while. I agree with that too (working it in among some kind of activity with others so she doesn't commit to a class or camp then get to bail for vacation with mom). Getting her out of her own house and away from anyone she could run into could help her open up.
One last thing. Is she changing schools for seventh grade? Around here, that is the start of middle school or "junior high" (sixth is still elementary school here) and it means the kid is going to a new school, seeing some old friends go off to different middle schools, worrying about who the new kids at the new school will be, etc. If she has to change schools this fall, she might be very worried -- and not telling you she's worried -- about losing friends, finding new friends, finding her way around school, doing well in class, etc. If school is important to her, that may be a factor here.
It does sound unusual for her to be this withdrawn if she's usually social and the change is sudden. If her past summers tended to be "chill" and she usually does stick around and hang out at home -- then this is a version of that. If in past summers she constantly wanted to see friends, then yes, this is a change and it does merit watching as school begins.