I think you should install the `-dev` package for GTK+3. On my more recent Ubuntu version the package is called `libgtk-3-dev` but IIRC it used to be called something else. It's the GTK+3 version of the `libgtk2.0-dev` one you list above.
When compiling with the official tarball, pass `--enable-gtk3` to the `configure` script so it will fail and tell you whether you have the GTK+3 stuff installed.
Most likely when Ubuntu 16.04 was released, the Geany packages were built with GTK+2 so using commands such as `apt-get build-dep geany` probably won't install the GTK+3 stuff you need.