For Ubuntu 23.10 and above, unfortunately you need to run GPlates from the command-line as:
QT_QPA_PLATFORM=xcb gplates
See this post for more info. It’s also mentioned on the download page.
This is a workaround for an OpenGL initialisation issue on Wayland, which will go away once we’ve finished porting OpenGL to Vulkan (for GPlates 3.0).
By the way, I will soon add a new GPlates package for Ubuntu 24.04 LTS so others don’t have to compile it.