To quickly introduce myself, I'm the main author of Paperwork. I've packaged Paperwork in various ways, and many people have packaged it in various distributions as well.
I'm fine with Flatpak. In my opinion, it has its use cases. I find complementary to other existing methods (distribution packages, AppImage, ...)
However I'm not fine with Snap. I haven't used it much, but my understanding is that it focuses on Canonical servers. You can change its configuration to use other servers, but it defaults to Canonical servers (and we all know most users will never change default settings). To me, this is a slipping slope towards proprietary services/software.
Moreover, I'm really annoyed by Canonical pushing Snap by default in Ubuntu (Firefox, Chrome, etc are packaged only using Snap now; the APT packages install the Snap packages). It doesn't bring anything to the users. Those packages could have been as well-packaged using APT (see the repositories *-updates in Debian for instance).