“if they stop living together i.e move out, but have not gotten divorced in the civil courts, they would still be considered married under bnei noach rules regarding adultery?”
I recall, there is a מפורש ירושלמי in Kedushin that if one officially moves out it’s considered divorced, and it works both ways not only the husband, she can say ” I want out’ and it’s over.
The same with marriage all you need is to officially move in as as husband and wife and they are considered married. See beginning of Rambam Hilchos Ishus the first halacha.