I remember my bunny Rucy doing the exact same thing your bunny did — try to eat greens, but then it was obvious she wasn’t able to take it in, just sort of rotated back out of her mouth, or she’d “pop” up in pain. I took her to my vet who said that the “spur” on her tooth wasn’t too bad, but that some bunnies are just a bit more sensitive to the discomfort. Rucy would also respond well to the pain meds. However, it was only until the spur (even if it was severe), was trimmed that she got back to normal. However, what did help in the meantime, until I could get her in was to cut her greens up into little pieces. Though sometimes the “pieces” would get stuck up on the spurs, like on top of shelf, for the most part, she was able then to consume them.
So you might want to try cutting up the greens into inch pieces or half inch piece or even smaller to see what works.
NOTE: Rucy also had root infections periodically and that caused pain when chewing. So that is something to ask you vet about. I know that at 13 years old though that it becomes risky. So obviously, you are the only one who can make this kind of decision for her.
Sending healing and hug vibes though for your senior bunny.