On Neon 20.04 sofware-properties-qt unable to open within the muon menu for displaying available mirrors.

It should run ok standalone, or from Discover.
I get an error that Muon is looking for the old software-properties-kde, which no longer exists, being replaced with the qt version.
This is most likely a bug in Muon/Ubuntu 20.04 packaging.

In any case, Neon probably won't or can't support Ubuntu/Kubuntu specific software.

You can just create a symlink called 'software-properties-kde' with target 'software-properties-qt'. That's what I did, and it works fine.

The dialog that tells you to install software-properties-kde is messed up visually too, with the markup tags as visible text.