Depending on how a school handled the 20-21 academic year, it could well have been an absolute wipeout in terms of social development and friendships (not to mention academics, athletics, mental health, etc etc etc ).
20-21 was our kids’ first year at their school. And it was really bad. Nearly 100% remote/zoom ‘teaching’ and extremely limited IRL interactions for the entire year. It was extremely rough on everyone but especially on those students entering that year, who of course did not yet have any existing support network at the school.
And, those “friendships” which did develop were so tenuous owed to the circumstances that they ultimately didn’t provide much of a base of support for many kids. At least not that we and our kids saw or experienced.
And then there’s the whole issue of being a day student at a boarding school. Obviously each school has their own % breakdown, and culture surrounding this. But the sad truth is that in terms of intergrating day and boarding students into a unified community, some schools make a very active, concerted, strong, and even successful effort to do so. Lawrenceville is a good example of this.
Other schools…not so much.
In your case OP, I agree with the others that the ‘off limits’ policy to even common areas within dorms is, frankly, insane. Not to mention actively exclusionary. Not only would I withhold financial support owed to this, I would make known explicitly my reason for doing so. I wonder if you couldn’t get a few other day student families to do the same.