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.