Saying the "self is an illusion" is a strange statement to me. An illusion implies something is being deluded. What is that something if not the self?
My takeaway with many discussions about self and Buddhism is just that it's a macro or emergent property, and not just one "thing".
Language can be imprecise but I think that's what is being referred to when we say self is an illusion.
When it is said the self is an illusion, what, exactly, is being fooled by this illusion if not my self?