Posting as a guest just in case this is weird but, I like to fiddle with things and my dog likes belly rubs. I sometimes absently find myself fiddling with one of her (very prominent) nipples. Is this a sex thing for her that I should stop doing? Or is this more like when I play with my partner's skin tags or pick at my scabs, which is what it's like for me?
Most probably not.
Humans are the only species which have fully developed breasts even before their first birth. There are many theories behind this. One that I found feasible for myself is that great apes used their buttocks as a sexual message. Therefore, the bigger the buttocks are, the more clear the sexual message is. However, large buttocks made mating harder, so humans, contrary to other great apes, started to mate from front. In response to this, human females developed breasts as a new sexual message. With the prominence of buttocks reduced, they got back to a mateable size (or penis size increased, I don't know), hence is the appearance of modern humans.
Erogenous zones are present both due to the dense nerve connection through the evolutionary process and the societal conditioning. (We usually cover erogenous zones.) Dogs neither have a reason for the dense nerve connection, nor have a society.
Finally, if your dog is neutered, the lack of sex hormones would also reduce any sexual pleasure she would get from her nipples being touched. In other words, even if they were erogenous for an unfixed dog, they are probably not for a neutered one.
I can give an example from my cat as well. When I first touched my cat's nipples, I thought it was a tick and had to look in close detail. I am not the only one getting confused this. My cat never did anything suggesting that he was ticklish or aroused.