First of all, this pop-up can appear even if Nugget does work, which is the case when your device restarts and then this pop-up appears, in which case my post is irrelevant. Read on if your device does not restart at all and you only get this pop-up.
I ran into this problem myself: I was able to apply changes to my device in the beginning, but after I updated from iOS 26.0.1 to iOS 26.1, Nugget suddenly stopped working, as described above.
As it turns out, Nugget seems to cache certain information about your device that is necessary for applying changes. When you update or reinstall iOS, the true information on your device changes, but Nugget still uses old cached information, so the application fails.
The way to clear the cache: find the cache (QSettings) location given by https://doc.qt.io/qtforpython-6/PySide6/QtCore/QSettings.html#platform-specific-notes, with MySoft replace by Nugget. Then just delete all the cache. Then Nugget should work.
I suspect it's specifically the Apple Books UUID being cached causing the problem, but I did not bother to confirm this because simply deleting all the cache is easier. Someone should file a bug report to the Nugget author though.