Signal does not require the phone to be online as well. Source: just switched my phone off and still able to send and receive messages on the desktop app. WhatsApp, however, still very much requires the phone to be online for its web/desktop clients to work.

That said, Signal is still not a "standalone" app on desktop because it needs me to have installed and set up the app on my phone to link it to desktop. After this though, they are very much independent clients.