Flatpak (by Alex Larsson and the Flatpak team) is the second in the trendy clique of complete-solution package managers. It is also a good way of packaging software so that one package can be deployed to any OS that supports Flatpak installations. Sound familiar?
Really, though, we are also getting into conflicting technology development (yet again) and holy wars (yet again).
To kick things off, I should point out that Flatpak really does emphasize desktop applications over server applications, from their complex run commands to the fact that they are mostly graphical tools. Snaps are definitely more of a mixture between the two worlds.
Obviously if you want to install a GUI on your server, there's nothing stopping you, you could even use VNC for management! However, it's not really done, like fish fingers and custard.