If you and your child prefer to have a low key time, I don't see the issue. That's not the Op's position though, her dd would love to do more stuff.
The thing is- the holidays are the only time that families can have holidays together now (with the new rules), to see extended family, to go back to homelands and so on. So, the children are socialising, but with different sets of people than usual. Plus spending time with parents when away.
People always remark on how sociable my children are and how outgoing, can chat with anyone, are quite popular, but this is not just their personalities, if anything they have slightly struggled to make new friends, so I have ended up supporting their friendships any way I can, from attending every party (I think one in 5 years we didn't go to), going to Brownies/Guides, having friends over just before the holidays, just before they go back, letting them text/build one or two really good friendships. If we just stayed home a lot and didn't bother doing much, they wouldn't be so outgoing or have so many friends. It comes very naturally to a few, the rest need a bit of support.
Op I think you have had some good suggestions on here on ways to diversify your dd's friendships out of school as well as within. I've found that really helpful with my two as sometimes groups of friends can really fall out at school, and it helps to have other sources of friends/activities to keep things steady.