The way I see it, it’s purely a terminology/nomenclature problem. Consciousness is whatever speaker decides to call so. When listener has a different notion, communication hits a barrier. Language works only because most have somewhat overall similar perceptions on semantics, and it’s easy for everyday stuff (and even then people can easily miscommunicate e.g. colors). Not that many think about nature of consciousness in any fine detail, so for most folks it’s just… a hand-wavy something humans have related to thinking and awareness.
And overhauling the language to match scientific understanding requires getting everyone onboard with that scientific understanding. Good luck with that, given that we have plenty of people who believe in weirdest nonsense.
Brain is not the only thing that makes us conscious, the whole human is a super-weird collection of highly intertwined systems that work together and produce whatever we call “human.” As I get it, it’s a huge complexity all the way down to that gut bacteria that somehow affects our thinking too. And I don’t think we have a vocabulary for all that - we mostly think of “self” as a single entity.