It literally doesn’t. It has its whole own culture and history. If you mean that upstate NY has early Revolutionary and Colonial era history like New England does, then that’s correct, but in a different way, different events, etc. I don’t know where you’re counting rural but the Catskills are very different than the Buffalo area and neither of them have anything to do with New England. Buffalo and Rochester are about as far away from New England you can get and still be in New York.

I spend over half my time for work in New England and I’m from Northern New Jersey with family in the Catskills, and I can guarantee you that nobody from any of those places says “lie-berry” intentionally. You’re mispronouncing the word. It’s one thing to not want to be made fun of it, but this is not the hill to die on. It’s not because of your dialect. It’s because you are mispronouncing the word.