I just updated the documentation for snapping a qt5 application. This includes how to use gtk-common-themes. This is a small qt5 demo application based on the documentation: https://github.com/galgalesh/snapcraft-desktop-helpers/blob/update-demo/demos/qt5/snapcraft.yaml
However, to be clear: as far as I know gtk-common-themes is not used to theme the qt widgets. It can only be used for the cursor and icon themes [*]. You still need a qt theme present in order to properly style the qt widgets and you need to tell qt to use that theme.
Another issue might be that the qt libraries are not where the desktop-launch script expects them to be. Take a look at this file: https://github.com/ubuntu/snapcraft-desktop-helpers/blob/master/qt/launcher-specific
[*] I might be wrong about this, because this is honestly all quite complex, but this is how I understand it.