A sidestory to this is that Flatpak and AppImage have been miraculous boosts to Linux OS machines. After I figured out that ya gotta throw the --user flag into your flatpak installs so they don't jam up your / tree, and also throwing flatpak override --user xyz.app onto a few apps that benefit from universal access, things have been fine and dandy.
I continue to be happy with how awesome Linux has gotten just over the past 5 years.
One thing you might notice is that flatpak defaults to "system" installs. Is your root system directory filling up? You probably want to start installing onto --user, as this will put things in /home where they belong and, by default, sandbox permissions away from root (that, too, can be easily changed).
Also, don't fear mixing different ways of installing. I use AppImage, Flatpak, the default app-get install method, and .deb. FlatPak at this point is the best, because it offers the ease of use of AppImage, but the flexibility and auto-maintenance of apt-get/Software Update. The only problems I've encountered were due to me not understanding that it was filling up my root partition by default...
I've been running Mint MATE for about 9 years. Love it to death.