I spent some time working on this problem, and I managed to determine that the application (Clipboard Indicator by Tudmotu) sends Shift (#16) + Insert (#45) and application compiled in QT6 registers it. However, after sending #16, the ssShift flag is not set in ShiftState in LCL. Therefore, the contents of the clipboard are not pasted, and the editor behaves as if Insert had been pressed. For now, this has led me to the DeliverMessage function in the QTWidgets unit, and this is where I stopped. I don't have the time or knowledge to solve the problem at the moment. I will try to delve into the subject, but in some time. For now, you can use the workaround I mentioned above.
Edit: in QT5 and GTK2 targets, the ssShift flag is set.