I mean, one thing I brought up before when talking specifically about Book Crowley, is that Fandoms sometimes kinda struggle with characters who have two (or more) seemingly-contradictory sides to their personalities (in Book Crowley's case, his coolness and his anxiety/fears). Either they get flattened into just the surface-level part of just one aspect of their personality, or this part is treated as nothing more than an unimportant 'facade' to their TRUE personality, when it's usually much more productive to see both sides of the character as 'real' and important.
So all of this to say, I do think that it's important to remember Book Aziraphale decides to kill Adam all on his own, it was his idea and his idea alone, and to accomplish that goal he tried to enlist Heaven and then lied and lied-by-omission to a pair of Humans to do his dirty work for him. This is obviously super thematically important to this story about moral ambiguity and an Angel and a Demon who became not quite Good and not quite Evil due to their contact with Humanity. It's a very important moment for Aziraphale's character in the Book and I fully understand the complaints when Adaptations reduce Aziraphale's agency in that decision for a maybe-more-standard 'Demon suggests something Morally Ambiguous, Angel doesn't want to" conflict.
But it's also important to remember that this doesn't make Book Aziraphale some sort of totally cold hardass pragmatist. The fact that it's the dorky Angel who gets a little too overeager to heal Bicycles who also resolved to kill the Antichrist while the Demon was still in "Step One: Get to Tadfield, Step Two: ?????????, Step Three: Profit" mode is pretty funny, but that doesn't mean that decision was easy or comfortable for Aziraphale. While most of his dithering and moral conflict is focused instead on his conflicting loyalties between Crowley and Heaven, he is also trying to convince himself Heaven could do the Child Murder in a way that's more… humane…
And he's also uncomfortable with actually Saving the Quiet Part At Loud in front of Heaven.
And then, of course, when it came down to it, he couldn't bring himself to do it. He might've been able to make peace with this worldwide Trolley Problem in the abstract, but it's quite a different story when you're seeing the kid in front of you and even your hitman is having second thoughts.
Which is also a very important moment to the Book's themes. Humanity has the potential to be more wicked than any Demon and kinder than any Angel. We have already heard a lot about how Human Evil can horrify Crowley, and here we have an example of Humans being the ones to inspire the Angel to be Good. And like, I know a lot of GO Fans have Problems with Shadwell and I certainly get it, but it is at least also thematically important that the Human that got Aziraphale to do the right thing was pretty unscrupulous not straightforwardly 'good' type. That's another one of Humanity's (and Free Will's) important qualities in Good Omens, people have a mixture of good and bad qualities, the same person can perform amazingly good and amazingly bad deeds.
Aziraphale can be hard, and he can be cold, but that little touch from Humanity got him to be Soft at just the right time to prevent them from killing a child totally unnecessarily and basically dooming the world.
Aziraphale's Arc in the Book is both about embracing moral grayness, but also about relearning his own Moral Center from the folks from whom true goodness and evilness really comes from, the Humans. That's why it culminates with him resolving to do something as selfless and seemingly as straightforwardly 'good' as a Heroic Sacrifice. Another showcase of how Aziraphale is good at making the Hard Decisions… Which he again, didn't actually need to make, but as I always say, it's the thought that counts.