For whatever reason there seems to be no Snap package of the desktop client available. But there is a Snap package of the Nextcloud server instead, although Snap was primarily designed for desktop applications. Well, we don’t have to understand everything, I guess…
Anyway, on Ubuntu I would prefer the PPA or the Flatpak variant, in that order.
I asume you tried to use the PPA. As I said, for the PPA you have to be at least on the latest LTS release of Ubuntu, which would be 20.04 Focal. But the message you posted, suggests that you are on Ubuntu 18.04 Xenial. Is there a specific reason why you are still using 18.04 on your desktop?
If you have to stay on 18.04, I would recommend using the Flatpak. But make sure you uninstall the old package or at least make sure that it is not running respective you’re not signed in anymore, before you use a package from another source