In my case, the reason turned out to be the fact that the plug-in was still using an ancient Info.plist file, without the AudioComponents section.
Once we added that AudioComponents section to the Info.plist file, GarageBand behaved as expected.
This means that, since my plug-in is not sandboxed, GarageBand showed the expected confirmation dialog where it asks for permission to lower its own security settings in order to load the non-sandboxed plug-in (details about this are here: Garageband X Sandboxing).
But ultimately the plug-in did load as expected.