Is Stolas disappointed that he didn't get executed? Hear me out.
During the "Mastermind" sing he sings:
"I am the mastermind, the master of my fate!"
It occurred to me this could be significant to his motivations, and the impact this has on him. Stolas's life has been defined by him not being able to chose who he is and what he can do, with Blitzø being a symbol to him of the kind of personal freedom that has been denied him. Seemingly because of Blitzø, Stolas has recently been stirred to exercise more agency in his life, such as divorcing his wife. And I think that desire to master his fate might be part of what drove him to do this.
It might be that to Stolas, giving up his life, and taking away from the hierarchy of Hell the service of the role he had been forced to play, this could be intended as an act of rebellion. A way of exercising agency so radical it will cost him his life, against all rules and expectations.
And so I suspect that aside from the humiliation, the loss of social power, wealth, and access to his daughter, what broke Stolas at the end of the episode is that his act of rebellion was invalidated. When he tried to give his own life to break some aspect of the system, he found the system did not even consider his life his to give. The hierarchy would not even let him die in defiance of it, rather, it simply re-asserted control over him, and took what it wanted from him.
I suspect he feels he was unable to escape being a cog in the machine, he is now seen as a broken cog, to be replaced, but still a cog. He thought he had finally become the master of his fate, but his fate remains the plaything of others.