Thanks for you reply! 
Yes, I use the default interpreter. python-gobject is installed as well. I can execute Python GTK programs just fine.
I also tried VS Code, there I couldn’t get auto-completion for GTK objects working as well 
Do you use VS Code at the moment, or what is your preferred IDE? Maybe you can give some tips how to get it working with VS Code?
Builder was what I tried first, which also doesn’t has reliable auto-completion for GTK objects: No auto-completion for python project in Gnome Builder