The extension authorization shows extensions that have been authorized (enabled) regardless of whether they are actually running. If an extension is running, then it will appear in the settings page.
Which R-PI 3 (B, B+?) and any Hats, Displays etc?
What OS install and version is running on the R-PI?
Are you running Deep Harmony as a docker image or did you deploy just the console app version? If docker, then which version of docker?
Same with the alarm clock as well? I guess that is running on a node install?
What happens if you disable one extension or the other?
As both extensions are disappearing then I assume something more serious is going wrong with the R-PI.
Deep Harmony even when directly installed as a console app is very self contained being compiled and makes no system changes whatsoever (the same is true regardless of which platform version). I do run it on my two R-PI 3B+ (Both currently have Rasbian on and Roon bridge on them). The arm docker image is Debian 9.5 slim based.
Edit: @support - this may be resolved, see Roon Extension: Deep Harmony - rich feature set for Logitech Harmony