The @hideifpath modifier (specifically the @hideifpath:!/desktop in my case) doesn't have any effect for the "Three Button" buttons (no matter if the sub-buttons also have this modifier or not). The "Three Button" button is always shown (but for example the @disablenosel modifier does work).
Not really a bug, just something that has never been supported.
You'd need the modifier on the button itself (not the sub-buttons), but there's no way to add modifiers to that currently.
Yup, that's what I thought, the modifiers (as a separate tab/category) can currently be added only on the WSH script buttons, something similar on the parent that would apply to children would be needed for the Three Buttons and similar.