There are two aspects to the Wrath Of God:
→ His judgment
→ His law
Most people confuse these separate aspects into one thing.
In Christ Jesus God satisfied His wrath of judgment against sin. Now, the only standard by which the wrath of judgment comes is based on how a person deals with Christ Jesus.
God's law has built in wrath. If a person breaks God's law, they will suffer the consequences of that violation which are built into the law that they break. God has to take no action or even thought about that kind of wrath.
The Wages Of Sin is death. What more destruction can their be than feath?
But those Wages are built into God's Laws. God does not literally get emotional when a person sins. Rather, He has built into the law the consequences of breaking it. It is seen as the Wrath Of God which it is in some sense. But His wrath is designed to destroy that which brings death so that only that which remains brings life.
20210910 update
Since we are in the Dispensation of Grace, God is not actively judging man's behaviour. HOWEVER, all of God's Laws have built-in judgment.
The Wages of Sin is Death. The Soul that Sins shall Die. Sow to the Flesh and reap corruption. God resists the Proud but gives Grace to the Humble.
I could go on, but the point is that we pay in this life for breaking His Laws. God set His Laws up this way to keep us inside the fence.
A rancher doesn't put up an electric fence because he wants to shock his livestock. He puts it up to keep them inside the fence. If one of his herd pushes against the fence it gets shocked and if anything the rancher is saddened by that.
The Dispensation of Grace will end when Jesus Returns. The Angels will Reap the Wheat and then Jesus will execute the Day Of Wrath to prepare the earth for the Millennial Kingdom.
At the end of the Millennial Kingdom the White Throne Judgment will come for all who have rejected Christ. All of those will be cast into the Lake Of Fire.
So, God's wrath is 1) built into His Laws and 2) will be unleashed during the Day of Wrath and 3) at the end of the White Throne Judgment.
God is Love and He is Longsuffering. He takes no Pleasure in the Death of the Wicked. But He is also Just and Holy and must Destroy those who reject Him, His Love and His Holiness as manifested in Christ Jesus. They would just mess up Heaven if He allowed them in.