In this case, "part" is not acting as a noun, but as an adverbial particle in the phrasal verb "to be part of". We could alternatively use "a part" as a real noun.

Both make sense to me. You could use "a part of" and it means the same - it may even be more 'correct' to use the article, but both are considered natural. This page says there can be a difference, but it's very technical, and most native speakers would use either form interchangeably. https://ell.stackexchange.com/questions/224909/difference-between-part-and-a-part#:~:text=The%20form%20%22a%20part%22%20emphasizes,of%20or%20an%20ingredient%20of.