It’s not an illusion. There’s not just not a 1:1 correspondence. But that doesn’t make it an illusion.
Reconstructed? Sure.
And consciousness? The flaw is using a noun where you need a verb or an adjective at worst.
You’re “consciousing”: it’s an active process or function. Or you could say a “conscious brain”.
But “consciousness” as a state is a mistake. There’s no noun as it’s active.