Chatgpt.com is essentially a CRUD app. What you're saying here amounts to saying that it could conceivably have been designed to work dramatically differently from all other CRUD apps. And obviously that's true, but why would it be?

It's a website! You submit text, that you'll view or edit later, so the server stores it. How is that controversial to a HN audience?

Also:

> the clients don't need to be running at the same time if you have a third device that's always on

An always-on device that stores data in order to sync it to clients is a server.