Hello,
I use a Linux distribution in which Dolphin does not show the custom icons, only generic AppImages icon
Do I need to install or build a specific KDE plugin for having custom icons being displayed in Dolphin ?
Yes. The file manager or some thumbnailer needs to suppport the AppImage format.
I think KDE nowadays should have a native AppImage thumbnailer. For example, Dolphin - Manjaro suggests that once you install ffmpegthumbs kdegraphics-thumbnailers qt5-imageformats kimageformats taglib libappimage raw-thumbnailer you should have AppImage thumbnails.
This is another option: