Jesus, the God of Israel, told Moses what to write in Lev. 18 and 20. He didn’t need to say anything; he already gave his opinion.
Indeed. I would also add another factor: while the four Gospels do not record a more specific example of Jesus specifically pointing to the sinfulness of homosexual behavior, I would say that was because it is highly doubtful that any 1st century Jew living in Palestine was arguing in favor of it. In other words, all Jews(Jesus, John the Baptist, their followers, Pharisees, Saducees, Essenes, Zealots, etc.) already considered it a sin per the Lev. 18 and 20 passages you referred. Hence, there was no viable argument otherwise.
On the other hand, Paul, the apostle to the Gentiles, was dealing with an environment where homosexual behavior was accepted more, i.e., the Greco-Roman world. Hence, he addressed it more specifically and directly and declared it sinful.