My reply is going to lead down a bit of a tangent...
If someone knows how to give you a more direct answer, then I would recommend you ignore mine!
I don't have a direct answer. But I have a long-standing curiosity about cross-platform development, so I took a moment to do a brief investigation.
When I need a point of reference for using Qt in a "massively cross platform" way, my "cheatsheet" that I often turn to is the Subsurface divelog project.
They are cross-compiling their Qt app on Linux to target windows. You can see their CI job config here. I know that's not the same as cross-compiling Qt itself.
However, I noticed (at the top of one of their scripts) that they call out how they are leveraging: https://github.com/mxe/mxe
And when I read the MXE page, I see they say: "MXE (M cross environment) is a GNU Makefile that compiles a cross compiler and cross compiles many free libraries such as SDL and Qt. "
Again, this is a very indirect stab and a mostly non-answer.
But if you end up in dead ends with anything you try, maybe MXE would give you a path forward.