Apparently you really like doing things in the most difficult way possible. Virtually no one does static deployments of Qt apps. Bulding a static Qt distribution just isn't worth the days of pain. It is far too easy to just bundle the required DLLs, which for a typical Windows GUI app are only 4: Qt5Core, Qt5Gui, Qt5Widgets, and qwindows, and probably the same on linux.

And as ChrisW67 says, even if you do get a static build, it may not support what your app needs. Some Qt things are only supported with dynamic libraries and AFAIK you can't mix static and dynamic libraries, at least not on Windows.