And yet most people call it a car, consider it real, and at the same time don't see a problem in reducing it to its physical properties.
"is the qualitative experience of consciousness actually real, or is it reducible to third-party objective facts"
Why not both?
The "real" refers to our subjective experience. That there is something that is like to be me. Something that is like to be a bat. And at least under certain definitions, that's what we call conscience. That something I know I experience and that I doubt a computer is experiencing too.
Why would this be incompatible with reducing this experience to third party objective facts? We simply don't know but I don't see why we couldn't.