@swoiwode
Yes, you have made the right changes! Note how you changed from PyQt6.uic.loadUi(ui_file, self), which loaded into self and gave you self.label etc. over to self.ui = PySide6.QtUiTools.QUiLoader().load(ui_file), which returned into a newly created self.ui (or whatever you choose to call it) and hence gave you self.ui.label etc. It's just a different way of doing things, and PySide just does not offer that parameter or loading into self.
Looking around at what examples there are on the web I found that actually even in PyQt more people had worked from self.ui = PyQt6.uic.loadUi(ui_file) which is also available and similar to the PySide way than that "non-standard" PyQt6.uic.loadUi(ui_file, self) which the code you inherited had chosen to use.
Honestly you came across one of the few difference between PyQt and PySide right from the outset in the small script you were working on. 99% of the time you should find that same code simply works from PyQt to PySide.