Canonical created Snapcraft for this very thing. It's a universal packaging system that allows you to package and deploy proprietary software. Snap daemon runs on any distribution and supports sandboxing. A couple of examples of paid apps on the Snap store are Mailspring and GitKraken, both of which I've purchased. Affinity Photo and Designer run on the Universal Windows Platform, so there's a good chance much of it was written in C#. The GUI elements can be ported over to GTK# on the mono framework if that's an option. Using Snap packages would allow you to deploy your application with all of its dependencies and any updates you submit would automatically be downloaded to every customer's desktop.
You can even allow your Linux users to provide you with valuable beta testing feedback by making a beta channel of each Affinity product on Snapcraft. I've tested snap packages on many largely incompatible distros with excellent success. From Ubuntu to OpenSUSE, Fedora, Arch, and Gentoo; Snap packages install and work all the same and render with the same look no matter what desktop environment you have installed.