I just launched the Dekstop app from their Debian apt repository. It says "Something went wrong! Failed to connect to server." and then the Debug Log contains stuff such as:

FetchError: request to https://textsecure-service.whispersystems.org/v1/config failed, reason: unable to verify the first certificate

Distro repos are notorious for containing super out of date stuff (especially when it comes to these kinds of apps). It's why we now have flatpack, AppImage and Snaps. Always check the version numbers when using repo stuff.

Bit of a stab in the dark here, but are you sure the repo is enabled and you're getting updates? I just realized I was using an outdated version because Ubuntu disables third party repos when upgrading.

It’s probably outdated, I know Debian is pretty conservative when it comes to package updates, have you tried getting it from signal directly?