OP, you mentioned above that she "constantly wants to be with others and we’ve allowed that, but at such a young age, shouldn’t she be having and wanting some time at home?"
Well, no, she's an outgoing six year old with a desire to explore and interact with the world. It's normal at her age. She's not a very young child that you can keep by your side any longer. You have to get used to the fact that this is going to be constant from now on.
At 6, it's natural to want to be with others, particularly as she's an outgoing
child. Being with other children is much more exciting than being with
parents! Since she's an only child, she's very lucky to be living in a friendly
neighbourhood, and I think you'll just have to get over your reluctance to
interact with the neighbours and accept that for your child's sake, you'll
have to chat with them and get to know them better.
You've repeatedly mentioned you want to be at home on your own, that you don't like interacting with the neighbours, you've mentioned frequently that you feel she should be spending more time with you, more family time. You seem a bit resentful of others intruding on your time.
It just appears that, because of your introvert character and your longing for her to want to remain with you, that she might not be getting all the social interaction that she desires. If she's outside on her own chatting with the neighbours often, how does that count as time with you anyway? Surely you should focus on quality time with her, and arrange that the rest of her time will be taken up with school and her friends and leisure activities?
You mention she plays with your friends' children, but you've said they don't live in your area, so how often do you see them? As an extrovert only child, you'd be acting in her best interest to encourage interaction with children most days of the week. Through playdates, classes, sports, clubs, playground visits, storytime at the local library, neighbour's kids, there are so many ways to get her interacting with others outside of school. As it has been pointed out, school is very structured. Playing with other children outside of school is so important for her development. Activities such as group sports can teach the importance of teamwork and cooperation.
Isn't it better for you all to have a wide range of friendships? I gather you don't want to foster friendships outside of the group you currently have, but can you not see the advantages of developing closer friendships with others, not just for your child but for you too? It's great to have some friendly neighbours you can turn to in an emergency, for instance.
You haven't mentioned school friends, do they visit or does she visit them?
Anyway, there's no need to answer my questions, they're questions for you to think about. I hope you'll read through all these posts again and reflect on what has been said here. Many posters have made valid points, so read through the thread again and have a think about how you might change things up. Your little girl seems to have a very different character to you, so you'll have to move outside your comfort zone to accommodate that.