while I find her annoying, I don’t believe I show it: I greet with a simple hi and proceed to do my job. I don’t look angry or exasperated at her, if you mean that. I don’t leave the coffee room when we do our pause and she enters the room. I simply don’t engage with her, but answer her questions politely.

Try talking to her - say you think she is a competent and friendly coworker. Say it might sound silly and weird but you find it hard and stressful to pull your head out of work to greet people, and say you hope she will understand you mean no ill if you sometimes grunt and nod.

Have you ever done this with a coworker? I don’t understand why I have to give validation to somebody who is, simply, a coworker, not a friend. I’m not a therapist.

I wouldn’t even know how to approach it. I would find it creepy.