rincor no native packages, and instead install everything as flatpaks
I did try this with Manjaro a few years back. It was OK, but flatpak feels considerably slower to launch compared to native apps. So, I didn't do it anymore.
rincor would it be like running on a freshly installed system forever, even after months/years?
Even you use flatpak for all applications, it doesn't replace any of the base system. It will only replace GUI application. The kernel, drivers, basic networking libraries and many more are still provided by Solus package manager that will be updated. So, no, it will not feel like fresh install after years or even weeks.
rincor Or does user specific stuff still inevitably pile up outside of /home even with flatpaks?
Flatpak store its config file in its own directory, either in /var or ~/.var depending on how you install it. Some flatpak even access your /home folder for config. So yeah, it will still scatter some file everywhere.