But you can now use them even if the phone is turned off, unlike previously where the "web" devices just provided a view of data from the phone.

The Signal desktop client has always continued to work even when the phone was off.

Interesting, I wasn't aware that was supported. Thanks for the information

Yeah, the implementation described in the article seems almost exactly how I understand Signal has been doing it all along. It's purely a client software choice not to allow a phone to be a secondary device. There's a fork which adds this feature to the Android app, though I forget what it's called.