It's just that the Qt company always tries to make it non-clear that Qt is not open source to drive their sales.
Regarding bloat, Qt is quite modular and if you want just the widgets you only need QtBase and none of the additional modules.
I'd go 100% native because that's how you make the best app for that platform. I also enjoy working with different toolkits and if I wanted this on more than one platform, I think I would enjoy designing and building it for different environments. For example the version I'd make for my small screen touch-based phone would probably be significantly different than what I'd want on my keyboard and mouse equipped big screen desktop.
A multi-platform or web-based solution would have too many compromises.