I would think anesthesia, in specific doses, would only attenuate consciousness...if it stopped other processes your organs and nervous system would stop. I guess this confirms that.
General anesthesia disrupts the ability of regions of the brain to network coherently. Individual regions might still be ticking along, but your experience of consciousness is a result of the network.
I’d argue that general anesthesia is the experiment that proves the fact. It’s a blunt and low resolution one admittedly, I wouldn’t use it to make any strong case about consciousness other than that our experience of it clearly requires coordination across many networked brain regions. As far as what’s going on within the individual regions or cells I’m not venturing a guess. Likewise I’m not claiming it to understand why networking of the whole brain is required to be conscious, but take some propofol and you’ll know that it is.