The KDE project has a few, some of which are Desktop and Android: https://play.google.com/store/apps/dev?id=475889458590528766...

Felgo sells Qt components etc (no experience with them), they have a showcase: https://felgo.com/showcases

Now I wonder if someone has made a big scan of apps from Play store analyzing what toolkits they use.

Not really a real-world app, but a simple QtQuick with Qt3d app worked pretty well. When it comes to app sizes, a vanilla Qt app produces an apk file of ~15MB, which is reasonable.

I had troubles accessing external storage (the SD-card), and ended up writing quite some ifdefs to fix that. Probably the kdab folks have proper solutions to most common issues, but at the end of the day the idioms between desktop apps and mobile apps are quite different, and you will end up wasting time to fix those issues if you really believe in having a single code base for cross-platform apps.

This is an app I've been using written in Qt/QML that works on desktop and mobile, it doesn't seem like there's a whole lot of differences to make it work on mobile: https://github.com/alamminsalo/orion

I had a Qt app for MeeGo and Symbian, and later ported and released it to Android too. I didn't like the use experience, so I rewrote in native Android some five years ago or so. Code was fine, but the UI was a lot of work and still felt a bit out of place.

Same here. Would like to see some real world apps and ideally also the code.