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The thing is, Aziraphale does see Crowley. He can see Crowley is on edge, he can see he isn't happy. There are many ways in which he is adept in reading expression and gesture (all those years through dark glasses), and the things Crowley does say, with the indirect speech they've both been forced to adopt. Aziraphale sees him and he knows he's not okay.
But they've switched roles, and Aziraphale doesn't know how to be the one who comforts and reassures. Partly it's because he's spent his whole life being afraid, and Crowley mostly wasn't -- Crowley was always the one saying never mind, they never check, they don't care who does the job so long as it gets done. Now Aziraphale is finally at a time in his life -- oh glory -- when he thinks he doesn't need to be afraid, and he doesn't know what to do with Crowley's fear. Just like he didn't know what to do with it when Crowley first asked for holy water.
And that's the other thing about Aziraphale: he's not okay with not being okay. Negative emotions are not okay. You don't feel them, you don't acknowledge them, you certainly don't discuss them. "Buck up, Hamlet!"
It's his flavor of traumatic upbringing, of course, but some of it is specific to Aziraphale himself. At heart, he's an idealist. Aziraphale believes in better. It prevents him having a fully reciprocal relationship with Crowley or even with himself, because only good things should be allowed, and if things aren't okay, then by God (yes), he will make them okay.