So I replaced Mint Mate with Debian:
https://cdimage.debian.org/debian-cd/current/amd64/iso-cd/debian-13.3.0-amd64-netinst.isoIt really doesn't appear to be that different from server-based one, that I tried earlier; about the same amount of basic apps installed out of the box.
What comes to appimages, although they include all dependency files, they may not work, if required version of fuse-related components aren't already installed.
On the other hand, another form of portable apps is to use either zipped or tarball (.tar.bz2) versions, if available. They don't seem to require mounting, or any extra system components to be installed, to be able to work.
An example in this case is Waterfox:
https://cdn.waterfox.com/waterfox/releases/6.6.8/Linux_x86_64/waterfox-6.6.8.tar.bz2To use it, first that file needs to be extracted. In file manager --> right-click --> extract here. Resulting folder is 'waterfox'.
In that folder is a file 'waterfox-bin', which is the actual executable. If it doesn't launch by double clicking, make sure that it has permission to do so, by right-clicking it --> permissions --> Allow executing file as program.
Another example is Mercury browser. which is a fork of Firefox:
https://github.com/Alex313031/Mercury/releasesI've used it as a secondary web browser since I started using Linux almost a year ago. It has never required anything extra system components to be installed either; it just works. Unfortunately it's bit outdated, but nevertheless, it has worked well for me.