If I understand the central argument, which is confusingly stated, the claim is that "consciousness" is a socially-determined, subjective, descriptor for certain things that one cares about. How does this make any sense? If I care about my teddy bear enough it'll gain consciousness?

Yes - the teddy bear would become conscious. It would be fair to dismiss the argument as silly and or absurd had it not been for the credentials of the author and the publication.

Your teddy bear, alas, is not cared for in a socially determined way. But you could create a church of your teddy bear and, with some grit, you could get people to widely assign consciousness to it. We have done that sort of thing for thousands of years, and not with fluffy teddy bears; it has been more often with rocks, though not exclusively. It's fun to think about how much of humanity's history and culture is the product of consciousness socially attributed to bad weather [^1].

I'm pretty sure somebody will create an improved synthetic simulacrum of self awareness in the coming years, suffering and all, just so that we can enjoy better synthetic software architects and product owners with "skin in the game". If that consciousness simulacrum were put in a teddy bear that shares your whole life and gives you decent advice and conversation, for how long do you think you could, in your private mind, deny it consciousness? Worse, what would your human friends think if you were to maim your teddy bear?

[^1] https://en.wikipedia.org/wiki/Yahweh

This seems like an argument someone who wasn't conscious would make, it's not impossible that not everyone is conscious. Or someone who takes panpsychism to an extreme degree.

If I stab at your teddy bear will you feel that it is hurt?

Yes it will gain consciousness. You can't prove it but other people can't prove that it's not conscious either