Signal's desktop does not require the mobile app to be active. Differently put, the desktop app does not depend on the mobile app's state. Mobile can be switched off/in airplane/far away from your physical location, but Signal desktop can continue to work.
For WhatsApp, the chats on desktop are e2ee too, but require the mobile phone to be active/online.
For Telegram, secret chats initiated on the desktop remain on that desktop app. They are not synchronized to the mobile apps.
Suppose I install and configure Signal/Phone, then install and configure Signal/Desktop, then turn off the phone.
Will Signal/Desktop still work while the phone is turned off?
* If yes, then what you say appears to be wrong.
* If no, then that's genuinely astonishing to me, and I've learning something.
Is there a grace period ?