When I download my app on AppStudio I got a Qt project. But I read the Qt framework is dual-licensed, available under both commercial and open-source licenses.
Qt - Legal | Obligations of the LGPL
So do I have to buy a licence if don't want release my esri app with open source license?
If you are using License version of App Studio, you don't have to license your app separately with Qt. Your App Studio License will do that work for you to publish your app.