It's buried pretty good, but I was able to back up in Windows and restore in Linux.

Make sure you go into the editor and save your avatar first.

You'll find it in %appdata%\Godot\app_useerdata\PNGTuberPlus   There will be a folder for each avatar you've saved.

In Linux they'll probably be hiding in ~/.local/share/godot/app_data/PNGTuberPlus/  Same deal - one directory for each avatar.

If you're running in Linux, you'll also need to chmod u+x PNGTUBER PLUS 1.4.5 LINUX.x86_64

Overall, it works quite well.  I can't get it to intercept my keypresses to change costumes but I look at that as a plus b/c I would change it accidentally more often than intentionally.