Anything you might install via Discover you can install with apt or aptitude. It's just a different interface. The problem likely is more or less transient, something that will go away at some point on via another round of 'apt update; apt upgrade'. In the mean time, you should be able to install a more familiar GUI package installer, Synaptic or Adept or another I never use.
If you search
https://bugs.kde.org/ you might find a bug has already been reported, maybe even fixed too, with the fix just not yet having reached the mirrors. If you don't find an existing bug, you could file a new report. Another place to search would be KDE's own forums or mailing lists, where someone might be familiar with the problem, maybe even have a solution.
Meanwhile you should be able to give Neon a more thorough shakeout. One package manager's boo-boo while alternatives work shouldn't be reason to quickly dismiss a whole distro. Remember, both Mint and Neon are built on a foundation of Ubuntu, which in turn is built on a foundation of Debian, and apt and dpkg. The primary difference is Mint's default DE isn't Plasma, while on Neon Plasma is. If you like Plasma, Neon should be a great distro choice.
