Unjapanologist

The role assigned to this robot certainly seems to correspond to that of a slave. And whether or not people would think of this as slavery may depend on whether people agree that she's conscious/alive enough to be recognizably human; if she is human, and she's being treated as property and forced to work against her will, that's slavery. If she's a machine, it isn't. My own gut reaction is that what we see here is a person; I didn't think of her as a machine for even a moment. Maybe that also has something to do with the fact that the first thing we see of her is her complete, human face. We don't see the face being assembled. The video sets us up to think of her as human.

Furthermore, what is the outside society like that gave birth to a market for all these Karas, not to mention the assembly guy?

A society pretty much the same as our own, I think. People are already trying to build these kinds of robots today, for the purpose of helping in the home, and most people don't seem to mind. As soon as home robots look lifelike enough, I'm pretty sure the first "functionality" expansion people will be asking after is to make them fit as sexual "partners". And I find it depressingly easy to imagine an assembly guy who likes to talk to his (female) creations as if they're human while believing that they aren't. If you're completely used to the things you assemble being machines...