Earlier quoted context omitted.
How is it related? AFAIK Signal has sync between desktop and mobile doesn't have to be constantly on to use the desktop client
Signal does have sync, but it works exactly the same way as Whatsapp's does, requiring your phone to be on and connected Telegram's secret chats are also client-specific and not synced, and I have no idea how it would even be possible to have e2e chats synced on multiple devices without having a "main" device that's doing the actual crypto or sharing the secret key
It doesn't. The phone is only needed for initial setup.