The "contract" I referred to when mentioning a Jewish definition of concubine (Jewish ketubah), has nothing to do with the marriage at a spiritual level - just as a marriage licence today has nothing to do with whether a couple are married. Think of it like a pre-nuptial agreement - it outlines things that are important to the couple for various reasons, and may affect how the marriage is conducted and property division on divorce / death, but it does not make the marriage. The marriage is formed by God when it is consummated.So could we essentially say a concubine is a woman has exclusive sex with a man and belongs to him but without a contract. And does he have to divorce her if he sends her away and out of his house.
In our society, we have "wives" and "de-facto wives" - but in God's eyes they are equal, and our responsibilities to them are identical. The difference simply relates to the social norms of today. Likewise, within the culture of ancient Israel, there were "wives" and "concubine wives" - and whatever difference there was simply related to the social structure of the time. In God's eyes they were the same.
God tells us how to treat our women / wives - all our women. Nowhere in scripture is that qualified to give any different instructions if that woman happens to be a "concubine", whatever the word means. The word is irrelevant when it comes to God's instructions around marriage.
As a wife, she must be treated as wife must be treated, according to scripture.