Adding to this, my kid’s preschool expects a caregiver around for all kids for the first 2 weeks. It’s a huge pain on scheduling (I also have a job and a younger child) and I’ve griped about it plenty, but I see the logic. Preschool is a huge change, a new environment, etc. It’s hard to adjust. I don’t think it’s unreasonable for a 2-3 year old to need to see a familiar face for a few minutes to help them calm down before reintegrating with the class.

OP, to you the suggestion that you are there may seem “punitive” and like they are overreacting to typical preschool behavior. But I’d venture a guess that this is something they do frequently to ease the transition into a school environment.