> Google Chat logs aren't direct p2p, they are most definitely logged records. Otherwise the messages wouldn't still be there when you log out and back in.

That's not how p2p works. Signal messages are not p2p but the server doesn't need to store them because the clients store what they've received. Same for pop3 email clients which talk to the email server (not p2p to the sender). Quite a few systems work this way that are not peer to peer. Not sure if you meant p2p literally or if it was a shorthand for systems that don't work like Telegram that store everything on the server forever (in which case I guess it must seem like I am just being pedantic, which I'm not trying to be).