OP punishing him for this at home (taking away his things) is just going to add to his frustration and anxiety.

Ask the school to give him his own safe calm down area.
Ask the school for an FBA.
Give him his stuff back and apologize.

OP it sounds like you don't have an IEP? It also sounds like you're punishing your child in a way that does not teach him the correct behavior. Changing his behaviors is about teaching him positive behaviors; not punishing bad ones.

As for the school claiming that "he just elopes; nothing triggers him" ... I don't believe it for a second. Believe what your son tells you -- that other children are overwhelming him. When my son was having behavioral issues I used to get SUPER frustrated when the teachers would report "He just all of a sudden hit a kid FOR NO REASON!!" What they really meant was "there was no acceptable reason and it wasn't right." Obviously there was a reason, but they were not bothering to actually observe it.

This is why you need a professional, ideally 3rd party FBA.

Can they create a partially walled off area in that room? DS's teacher put a few bookshelves to create an area where 1-2 kids can sit quietly and can slump down and not have to see the rest of the room. The teacher can still see in when she's standing up so it's easy for her to supervise.
The teacher did not create this as a safe space for DS but he uses it often and she told us that numerous other kids use it too. She hasn't had any issues with someone being in there and someone else wanting to use it.

He needs his own safe space!!