Thank you everyone who tried to help to resolve my problem. The answer came from official Qt forum. Link to solution: https://forum.qt.io/topic/127696/qt-qpa-plugin-could-not-load-the-qt-platform-plugin-xcb-in-even-though-it-was-found/22
Basically, the problem was in lack of some dependencies. Because of specificity of Qt6 I had to install dependencies from Qt5 building manual. It’s hard to say lack of which dependency caused the problem, but after installing all of them and reconfiguring and rebuilding source code, project builds properly.