I think the confusion comes from the fact that you are trying to apply the modern construction of marriage to a non-modern setting.
“Legal union” has no meaning for Adam and Eve. Their marriage is given to them by God, who makes Eve FOR Adam. As the church develops and especially after Jesus is sent to teach us how to follow God, we come to understand the place and meaning of the sacraments (which is the important aspect for Catholics - that the marriage is sacramental) and moreover, how those sacraments are to be administered.
Rather than thinking in the context of a “legal union”, it is more helpful to think of it as a “valid marriage”. For Catholics, the only valid marriage is a sacramental marriage - you might be able to have a JP marry you civilly, but you are still obliged to be married in the church if you want your marriage to be recognized in the church. That is what our faith teaches. If you are Baptist, and your spouse is Baptist, then a church wedding may not be necessary to be considered valid in that faith (I’m not sure if this is true - I just used Baptist as an example). If neither you nor your spouse are baptized, then a civil ceremony creates a valid marriage.
So rather than looking for a “legal union”, look to see if the marriage can be considered valid, having regard for all the circumstances of the time and the individuals involved.