> Using the same hardware for both would be super useful, but the software stack from the desktop environment upwards should be entirely different (yes, including most of the applications!)

Phosh (Phone Shell) already exists and works quite well. I'm writing this comment from desktop Firefox running in Phosh on Librem 5 smartphone.

See also: https://videos.puri.sm/pureos/l5-convergence-purism.mp4