It seems, indeed, the issue is related to GTK-2. I'd installed Debian testing (bullseye) and tried on it the same Geany v1.37 clone (now developed) - and voila, no issue of Overview!
Geany in Debian bullseye is Using GTK+ v3.24.13 and GLib v2.62.5 runtime libraries
Nevertheless, it's a pity that the Geany's plugin doesn't work properly in the stable (not so old) version of Debian and probably in its numerous derivatives. The Overview plugin is very good, especially when used along with the Git change bar plugin.