My dd had this going from room 2 to room 3 (out of 4) at her nursery. She really, really struggled even to the point of mild self harm (scratching till drawing blood). She'd previously been so happy in rooms 1 and 2. It was a dark time for us, maybe the hardest period of parenting I've ever had (so far...!)
We got through it with some really close communication between us and nursery, who tried lots of strstegies till things got better, which they did, in just a couple of weeks.
My concern from your post is that the nursery isn't making suggestions of solutions, only presenting you with the problem.
Our solutions were totally unique to my dd but fwiw, they were as follows.
Dd doesn't like noise or bustle so they gave her a quiet corner with a chair in it, and that was her quiet corner to retreat to when overwhelmed. We changed which clothes she wore (no zips or hoods) as she was hurting herself fiddling with the zips till her skin bled, and she'd hide this under her hood. She was given helpful "jobs" to do like tidying up, which cheered her up. I insisted that the staff check for scratches frequently, as once, they'd left her with blood on her neck which dried there, it had been hidden under a hood. She didn't like being greeted in the morning with a hug, so they greeted her with a personalised "Hello Name" song which she preferred. After a couple of weeks of these strategies, things got way better and she never scratched herself any more. She loved going in after that. The song thing in particular was such a breakthru, I've posted on it on MN before.
Then when it was time to transition from room 3 to room 4, they over-planned it like a military operation, with settling sessions starting months before, starting with just a few minutes at a time. (Unlike the rest of the class who just transitioned with a single half day settle the week of the move!) It worked totally fine, no issues.
That's how the nursery ought to be dealing with it.