They committed abomination as one of their sins, per the rest of your
Ezekiel 16 text, which you didn’t seem to want to include:
Behold, this was the iniquity of thy sister Sodom, pride, fulness of bread, and abundance of idleness was in her and her daughters, neither did she strengthen the hand of the poor and needy. And they were haughty,
and committed abomination before me: therefore I took them away as I saw good. -
Ezekiel 16:49-50
This kind of abomination:
Lev 20:13 If a man lies with a male as with a woman,
both of them have committed an abomination; they shall surely be put to death; their blood is upon them.
Jude confirms that sodom was destroyed for homosexuality:
ISV:
Jud 1:7 Likewise, Sodom and Gomorrah and the cities near them, which like them committed sexual sins and pursued homosexual activities, serve as an example of the punishment of eternal fire.
Genesis has the account of their homosexual activities and wanting sex with Lots male guests:
Gen 19:4 Before they could lay down, all the men of Sodom and its outskirts, both young and old, surrounded the house.
Gen 19:5 They called out to Lot and asked, "Where are the men who came to visit you tonight? Bring them out to us so we can have sex with them!" ISV
It’s clear to me that the scriptures focus on homosexuality being the reason for the destruction of Sodom.