Doesn't fit the part about licenses that restrict what you can do with your code:

"Qt for Application Development is dual-licensed under commercial and open source licenses. The commercial Qt license gives you the full rights to create and distribute software on your own terms without any open source license obligations." https://www.qt.io/licensing/

One of the "open source" licenses that it is under is LGPL, you can do whatever you want with your code. (Although this does not mean that you should, please avoid publishing closed source software)

It's not a bad suggestion, but it still doesn't satisfy the requirement. You can't put it all in a single executable if that is what you want

You can, as long as you give the user the ability to replace the library. Such as by providing .o files.