Linux

This kind of integration testing is best left up to the individual distros. Same as the integration (as in: packaging) itself.

Distros don't want your binary package, they want your source code, build instructions and a build system that won't make them cry. Some distros even explicitly disallow re-packaging external binary distributions.

As a distro maintainer, I appreciate your wish to do QA on all the distros but that's just too much work. You focus on making your software better, we focus on making it work with the rest of the software ecosystem.

Providing a package for one or two distros (i.e. your favourite one) is good practice to ensure your software can be reasonably packaged but it's not the primary way your users should receive your package in the traditional Linux distro model.
Additionally, you might want to package your software for one of the cross-distro package managers such as Flatpak, AppImage, Snap, Nix, Guix, distri or homebrew. This can serve distro maintainers as a point of reference; showing how it is intended to work so they can compare their packaging effort. If there's some bug present in the distro package but not the cross-distro package, that's a good sign the issue lies in the distro packaging for example.
Again, don't put much time in this. Focus on your app.

https://Open.qa it is an OpenSUSE tool but it can be used to auto test installs of any OS/software. Their open build service also automates and tests package building

I think there would be a way to test it with docker, you could find a image that has systemd installed and use something like distrobox to test it with the GUI.

Not mentioned here so:

• virt-manager is better than virtualbox.

sudo dnf install qemu qemu-kvm virt-manager
sudo groupadd libvirt
sudo usermod -aG libvirt $USER
systemctl enable --now libvirtd
virt-manager

Thats the way on Fedora, debian packages are called a bit differently, Ubuntu again, but that method works.

Also for packaging an app that just works, why not flatpak? Especially if its a GUI app, this would highly improve availability on many Distros not covered by RPMs and DEBs. Also RPMs can have dependency conflicts between Opensuse and Fedora because naming, probably similar with Ubuntu and Debian.

If it were me and I was intending to automate this I would probably do the following. Set up each test distro as a VirtualBox image and take a snapshot so I could easily roll back. Then I would write a script for each distro that downloaded the package, installed and launched the app. I would then probably query the window system to make sure the gui showed up, wait a period of time if I had to and take a screenshot.

This can probably all be done as a set of bash scripts.