I think it's 100% fair that even outside of a Butchlander interpretation, it's an expression of relief.
He just lost his son. He realized that nobody will love him, ever. The world has been lost to him. In the moment he loses it on-camera, he knows this is the end. The world will hate him until the day he dies. He is forced to be a loathsome monster now. Ryan won't ever speak to him again. Neither will Soldier Boy, should he ever wake from his pod.
So here's Butcher. The one man who never broke a promise to him. The man who came for him. The man who is thinking of him all the time. The man who has dedicated his life to him in a way that nobody ever could. The opposite of love isn't hate, it's indifference.
Butcher has not been indifferent a single day.
Scorched earth is STILL ON. And while Homelander is deluding himself into ignoring what scorched earth even really means (that only one of them will be leaving the White House), he knows one thing: it's the most intimate thing he has to look forward to now.