If your appimage is from gimp.org (which is now publishing them) the plugin does not work. However if you get the ivan-hc appimage from:
https://github.com/ivan-hc/GIMP-appimage/releases
look for the section:
Continuous Developer builds (JuNest Arch Linux-based AppImages) Pre-release
and download:
GNU-Image-Manipulation-Program_DEV_3.0.0rc2-1-archimage3.5-x86_64.AppImage
Then download
resynth-gimp3.zip (77.1 KB)
Then extract the contents of the zip folder to the /.config/GIMP/3.0/plug-ins folder.
I’m using this method on both linux mint 21, and 22 and Resynthesizer works as it should.