yes, but I think it just generates a keypair for that and then autosigns whatever messages it creates, so the user experiences no friction -- they don't have to copy/paste anything to and from their node, for example

That's correct. Also nothing stopping either party from using their own keys if they prefer.

I'm just being a bit pedantic because a signed nostr message is essentially the same thing as a signed message from your node. Only the UX is different; it's not about there being an "account" from a technical or privacy perspective. it's that there's user friction in signing messages.