And Smaug, who is treated with some disdain in that he hoards precious things but has no regard at all for their value. So there's arguably a fourth category there.

I wonder if this is highlighting how different Bilbo is to the others, and also how useful this makes him to them – he ends up seeing things the others don’t see because he is conscious at different times (and he does literally have better eyesight than the dwarves as well).

I love this reading of it a lot.

The naming of Sting is, I think, one of Bilbo's major turning points (between the mirrored besting of Gollum in the riddle game, and his riddles with Smaug). It's also the point where the Dwarves start expecting him to have the answers - which he does manage, in the end. I second your Hobbit feels because agehagoehawl; Bilbo absolutely rocks in this chapter.