Nero being emperor when Romans was written only proves that a wicked, psychotic, pagan ruler can possess God-ordained governmental authority. It does not prove that the wicked ruler's every act suddenly becomes "God-ordained righteousness".
Thats the distinction.
Jeremiah calls Nebuchadnezzar God's “servant,” yet God later says He will punish the king of Babylon and that nation “for their iniquity.”
So being used by God does not make a ruler righteous and possessing authority under God's providence does not make every command righteous. Executing a legitimate function of government does not turn every murderous atrocity committed by that government into "divine justice".
Romans 13 does not say, “Whatever Caesar does is good because Caesar is in power.” Paul describes the proper function of governing authority --- restraining evil, punishing wrongdoing, and maintaining order.
And yes, Paul wrote that while Nero was emperor and that actually strengthens the point.
Nero could possess real governmental authority without being a righteous man. Nebuchadnezzar could be called God's servant without being a righteous man. God can use wicked rulers without calling their wickedness good.
The same principle applies in the West today.
The fact that rulers possess lawful governmental authority does not make them righteous, and it certainly does not transform every corrupt, destructive, dishonest, or wicked policy they pursue into the will of God.
Authority is not righteousness.
Providence is not endorsement.
God using a ruler is not God approving everything that ruler does.
The Bible itself makes that distinction.
Thank you. That‘s my position. You’ve stated it well.