Here in 𝓟, Oliver Cowdery wrote poverty as poverity. Although normally Oliver wrote the word correctly (five times in 𝓞 and six times in 𝓟), he occasionally miswrote it (but only in 𝓟) as a word ending in -ity, here in Helaman 13:31 and two times earlier in the text:
For these other two instances, 𝓞 is extant and correctly reads as poverty. Thus Oliver is the one responsible for poverity; it does not represent some kind of archaic or dialectal form for the word poverty (nor is this form of the word found in the Oxford English Dictionary).
Summary: Maintain the word poverty throughout the text; in a few places, Oliver Cowdery wrote the word as poverity in 𝓟, but that form of the word is clearly innovative and not original to the Book of Mormon text.