If one were to study that, I don't know if homeschoolers are the best group to look at. Also, it's tricky because there is a big difference between healthy socialization and unhealthy socialization. Are we talking about being completely alone or being in a huge group with no friends?
I don't know that this would work so well because lack of socialization is one of the biggest myths about homeschooling. The homeschoolers I know hang out in the park for hours 2-3 times a week, do skill shares together, take classes and electives, travel the world. This pandemic has been harder , if not more so than other groups, because they can't use the world as their classroom in the way they've done before. Also, many children struggle mighily in school. Just because there are lots of people there doesn't mean kids don't feel incredibly isolated. A bad social experience (Eg being bullied and isolated in school. Bullying and systemic racism run rampant in our schools. Teachers are exhausted spending most of their time managing behavior rather than getting time to teach and facilitate healthy social-emotional learning in the classroom.
I started a digital pod this fall and some of our kids didn't say a single word in class last fall. Now, in a group of 5-6 kids they are actively participating, sharing their hopes and dreams. Some communicate verbally, others prefer to observe.