A man could have more than one wife in the OT, Deuteronomy 21:
Deuteronomy 25:
The brother of the dead man could already have a wife of his own and take on one more wife.
2 Samuel 12:
God permitted David to have multiple wives and gave him wives.
What about in the NT?
English Standard Version 1 Timothy 3:
1 Corinthians 7:
Polygamy was permitted in the OT but discouraged in the New. Matthew 19:
The moral framework for marriage/family/sexuality matters is the Torah, both for TNK/OT times and for New Covenant/NT times (see Acts 15 where the Jewish Apostles/elders use this as their framework of reference).
In New Covenant/NT times we see that Yeshua highlights that our thoughts/mindset/heart ultimately guide our actions. So a physical sin starts with a mental sin. But the moral framework wasn't changed (Paul argues it is still the Law/Torah that defines sin). We see John mentioning 'a new commandment to love one another', but that is an expansion of Leviticus 19:18. The New Covenant/NT does not introduce new prohibitions - it relaxes some of the old ones.
Based upon the following I would argue that it wasn't a sin in TNK/OT times and in all likelihood neither in New Covenant/NT times:
- the Torah doesn't prohibit it while a man having more than one wife was common throughout ALL Biblical times
- the Torah regulates matters in cases where a man would obtain an additional wife (if it was a sin it would simply ban it altogether)
- the Torah's levirate instruction even is a
command to take an additional wife in case the surviving brother already was married (as you've already pointed out)
- YHWH portrays himself as a man having two wives in the books of Jeremiah and Ezekiel
- the Torah condemns the multiplication of horses and wives for Israel's kings, but that doesn't mean having two horses already was a sin
- David's sin was called out by God through the prophet Nathan - the accusation is clear; besides murder it was a case of adultery because
Bathsheba was married, not because David already had multiple wives at that point - God even indicated He had no problem with that
- men having multiple wives (Abraham, Jacob, Gideon, David) are included in the 'heroes of the faith' list in Hebrews 11 (if polygamy was considered to be adultery in New Covenant/NT times these men would not have been included)
- no man in either TNK/OT or New Covenant/NT books is ever condemned/called out for having more than one wife
- the New Covenant books contain veiled traces of Polygyny:
* 1 Corinthians 5:1 refers to someone's 'father's wife' instead of mother
* 1 Corinthians 7:2 uses both an 'exclusive' term for 'own' (wife) and a non-exclusive 'own' (husband)
* on three occasians Paul gives instructions that a separated/married woman is bound to her husband, but nowhere does he write the reverse for a man. The obvious explanation for this 'unfair/sexist' asymmetry is that Paul is emphasizing compliance with the Torah on marriage/sexuality matters. The Torah didn't allow a woman to have more than one husband, but it did allow a man to have more than one wife.
Polygyny in Judaism was banned for European Jewry in the 11th century by Ashkenazi Rabbi Gershom ben Judah (960-1040 CE) and would last a thousand years - that ban has now formally expired. That ban was not introduced because of theological reasons, but to avoid problems in German society in those days. This ban was never recognised by other Jewish groups like the Sephardic.
As long as a husband keeps his marital obligations and his able to follow Paul's instructions regarding his wife/wives and things are consensual I would not call this sin. To introduce a new moral prohibition and label that 'Gods Law' for me would be like 'adding to scripture' in an unauthorised manner.
It would be rather strange and unexpected if a drastic new moral prohibition would be introduced to New Covenant/NT times believers ONLY in the form of a byline as part of qualifications for elders/deacons, because it would represent a radical break with the Torah. Monogamy was the formal norm of the Roman Empire, not of Israelite/Jewish society.
Unfortunately this topic is highly divisive - the Achilles heel seems to be the concept of Patriarchy; Polygyny requires Patriarchy in order to work. So egalitarian believers who oppose Patriarchy therefore also have to dislike Polygyny.
For a deeper scholarly treatment of this subject I would recommend reading:
On the Morality of Biblical Polygyny (by Professor (ret.) William F. Luck)
Maybe good to add it doesn't seem to be God's ideal for Adam - he only was given Eve. Number-wise societies with equal numbers for men/women run into trouble when many men can't find wives because the high-value men hord wives. Also consequentially the amount of time a man and his wife share is less than in a monogamous context.