I ran into a very similar problem. using the install.sh does make a 1.21.6 version, but the 1.21.5 version was still there, also the new version didn't have access to my save files but the old one did. In addition to what you did, I also used flatpack to uninstall VS with
flatpak uninstall --delete-data vintagestory
and confirming Y to everything. I reinstalled Vintage Story via install.sh and used the default file location. I was even able so move my save files away before deleting, then moved them back into the saves folder and they still work. I only recently started using Linux Mint so maybe there is a better way.
