I take it you’re talking to @cscs, since I didn’t get notified, but here goes anyway.
If you’re talking about qt5ct then it’s already installed by default in mate, but kvantum isn’t.
Your solution involves installing qt5-styleplugins which of course contains plugins for QT. So I guess installing more QT is a solution as far as you’re concerned. 
It’s also in the link in my post, which admittedly wasn’t there when you initially posted.
The problem is that you’re using two different toolkits, of course it’s going to take work to make things look the same, and in some cases it won’t be possible.
Perhaps that’s because everything else uses GTK or another toolkit. If you want things to match stick to a single toolkit.
Also most software in KDE is made by KDE, whilst most other software is made by random people.
GTK2 is not a real solution, it will stop working eventually and of course it isn’t the same as GTK3 or GTK4 so it won’t always look the same. It also needs a theme that is compatible with both GTK2 and GTK3.
Indeed.
You don’t need a global environment variable. You can accomplish the same thing by setting it in qt5ct aka Qt5 Settings. However it requires a compatible theme.
EDIT:
If you haven’t already seen it, you might want to look at this: