According to a Catholic teaching, whether Thanos did anything wrong

Probably his sin was "pride". He consider himself able to decide on other lives, and to establish which is good and which is not: only God can do it.

Just like Adam and Eve after eating the forbidden fruit: they started to doubt God's knowledge of good and evil .

It's the first sin, and maybe the worst.

To continue after the manner of Aquinas:

On the contrary, Our Lord says (Mark 10:19) "You know the commandments: 'You shall not kill'."

I answer: The natural law, as its name implies, is written into nature. It is given not only to those who have been baptized into the family of Christ, but to all rational beings:

The natural law is written and engraved in the soul of each and every man, because it is human reason ordaining him to do good and forbidding him to sin. (Leo XIII)

Though written of human beings, this clearly applies to all rational beings. It is therefore incumbent on Thanos to follow this law.

Now we are told that it is never moral to commit an intrinsic evil even in pursuit of a good end; and clearly to kill another is an intrinsic evil. But the desired end, as shown, is undoubtedly good, perhaps the best imaginable physical good. Why then is this action immoral?

An action is good insofar as it disposes one toward God, and evil insofar as it turns one away. To kill, then, is evil, because it shows utter disdain for the life of another, rather than the love shown by God. Thanos, regardless of his motive, is showing the highest consideration for the universe as a whole, but none for the individuals whom he consigns to death. "If a man has a hundred sheep," Our Lord said, "and one of them goes astray, will he not leave the ninety-nine in the hills and go in search of the stray?" Or again he says that not one sparrow falls to the ground without His Father knowing, and tells us that we are more than a thousand times as valuable. If Our Lord shows so much solicitude for each one of us, must we not do the same? But killing - killing half the universe - ignores the natural dignity of each rational being, and the love that we must have for not only all, but each. This the natural law makes it evil to set out to kill, no matter what the intention.

Response to Objection 1: Any mention of "the greater good" are of doubtful worth in an argument. Many have spoken of "the greater good" only to inflict evil in others. In addition, it is not sufficient to point to the greatness of the good to be accomplished. The natural law is a reflection of God in the universe. Its application must be consistent with God's nature. And as God cares for each one, so too e must care for each one. Thanos did not do this.

Response to Objection 2: As above, it is wrong to intend to kill, and this seems to be what Thanos was intending to do. It is excusable to take an action which may, or even will, cause death as a side effect. In this see one is simply working to help or heal, even though death is incidentally caused. But this is not what was done.

Response to Objection 3: The objection, in essence, is that Thanos has no choice; that nothing else could have been done. It is not entirely certain, though, what the limits of the Stones' power is. Nor is it at all obvious that Thanos has explored them with the intent of avoiding the outcome he presents as necessary. There is no reason to believe that Thanos has no alternative path of action.

Response to Objection 4: Certainly eugenics, the philosophy that people's lives are to be treated according to some human standard of relative worth, is reprehensible. It does not follow that any other method (e.g. a random method) of selecting rational beings to be killed is necessarily not reprehensible.

Response to Objection 5: Indeed we are told "All things in moderation." But there is nothing moderate about killing one person, let alone half the life in the universe. Moderation regards quality of action as well as quantity.