A category made up of 1 the Statue of Liberty 2 The current Pope and 3 my toothbrush, for all its insane bagginess, and poor fit to reality is made up of things which themselves exist. So it’s much too hasty to conclude lack of reality from poor fit.
Yes, I do think consciousness is such a category. The OP mentions, under the heading of consciousness, issues of what I would call personal identity and qualia. I can’t think of any reason why having the one would grant you the other.