No you're right, I was slightly worried about the usage of p2p and was expecting someone to correct me. Apologies for using the wrong word.
I was referring to the fact that self-destruct messages in Google Chat can be seen within 24h regardless of which device you log in with, this means it has to have been stored server side.
Signal has multi-device self-destruct also, even to a few seconds, but that doesn't mean that you can't see it anymore on your laptop if the phone in your pocket fetched it and your laptop was rebooting. The message is (as I understand it) addressed to both devices, probably Signal doesn't even need to know whether the recipients are one account or whether it's a group chat, or that the message has a self-destruct timer set on it. The server just stores messages until the client for which it was intended has fetched them (with some maximum, I guess). Google's chat could work the same, but I'm not sure we can know that. The server software is probably not open source.
I was referring to the fact that self-destruct messages in Google Chat can be seen within 24h regardless of which device you log in with, this means it has to have been stored server side.