any possibility that I may have damaged a wire in the wall?
I have seen many damaged wires inside walls when remodeling, some with the outside jacket and both the conductors and ground exposed. Some have even damaged the wires because of visible arcs I know the breaker was tripped. Others just skinned the wires or the jacket (this doesn’t include the wires I was called to repair where they were severed in the walls). I was quite surprised on a few that they continued to work. All of this said it takes quite a bit of friction to cut through a unsupported piece of Romex. It sounds like you were careful and if you cannot see any damage and did not trip the breaker or GFCI things are probably ok. I would check the light and fan as that could have been a switched cable and the reason it did not show as hot was it was turned off. Then we can think of all the calls where the wires were cut. I would not be worried about most plastic anchors except the self drilling type. Of course the only way to know for absolute sure is to open the wall or use a bore scope to inspect but my guess with no arcs and sparks , tripped breakers or getting shocked if everything still works it’s probably fine. The last quick thing is all of these anchors are usually shorter than 1-1/4” the romex is supposed to be in holes or stapled that far back , so it was probably flopping around making it harder to cut through the insulation.