Curate, connect, and discover
Crowley wanted Aziraphale to see that he had saved the goats. The way he looks back, how easy it is for Aziraphale to lift the miracle, he wanted to be caught by Aziraphale. We see how well the hiding miracle worked on Gabriel, the crows bleating was more than just a tiny slip up. It was intentional.
It’s the same with how he wanted Aziraphale to say to him that he believed he would save Job’s children. He’s so desperate to be seen for who he truly is in those moments. Even with the fake tough outwardly persona, he wants to know someone has faith in his true nature. Which is kindness.