@rsramkis whilst its probable that Geany is using that version if its the only GTK you have installed, just `Help->Debug Messages` tells you what GTK Geany is actually using at runtime (for the experimentalists with more than one version of GTK installed).
You should be able to select the backend by starting Geany `GDK_BACKEND=x11 or wayland geany` to determine which is actually being used, and also to try the other to help isolate the problem. Of course there is also the issue of what the other end of the copy/paste is using and which type names it accepts.
I can't find it just now, but somewhere a command that shows whats on the wayland clipboard is mentioned on one of the myriad of issues about Wayland and cutting/pasting, maybe that helps you to find it and see if the right thing is being made available.