You can’t move “var” to a “System files” folder. This would break programs which expect /var to be, well, at /var. Long ago on macOS, everything was in “System Folder”, and it worked fine, but macOS has since inherited a massive Unix legacy.
Thumbnail caches are not stored on USB drives, they’re stored somewhere else, away from your files.
There is no need to hide such files. Just display them as system files in Explorer.
> The standard Unix folders (usr, var, etc) are also hidden
Again there is no need to do it. Just move them to a directory named "System files".