hazzy uses PyGObject to access all the GObject-based libraries (like GTK) from python. My guess would be that you have successfully installed GTK+ 3.22.0, but don't have the corresponding version GObject installed.
You should be able to check the output of `$ apt-cache policy libgtk-3-0` to verify the version of GTK+ you have installed.
I am not sure what the best why to install PyGObject is. You can probably install it from source from here:
www.gtk.org/download/linux.php
TurBoss mentioned that PyGObject can now be installed via pip, but I have not tried that. Probably best to use a virtual environment if you give that a go. It also might be worth trying `$ apt-get install python-gi-dev --dry-run` and see what it looks like it would install.
What OS are you using? I might install it on a test machine and see what it takes to get GTK 3.22 installed and hazzy to run.
Sorry I can't provide any better help, I am still new to all things Linux.