To me, there’s no big difference between stateless and stateful, because the purpose of a signing device is to protect the keys from leaks during use. In between uses, other key security measures apply (physical security, operational security).

I would not reuse a signing device for multiple seeds though. Especially seeds that make up a wallet quorum. One hopes that each device’s erase function works, but it’s safer to assume that they’re each forever stateful.