I can offer some context and input but will acknowledge that I don't really like how this matter was done nonetheless. It does involve a genre shift, just a different way.
I was not a fan after the book. I read it in October 2018. I liked it well enough. I can see that since I don't read many books, a lot of it stuck with me in my own fanfic writing not long after I read it. I read it at least once and then probably either re-read it or re-read some passages because it's such a big ensemble piece. I have re-read it twice since watching the show.
I didn't walk away from that book thinking that a big theme was "Read between the lines, and figure it out for yourself," or "discernment" as another Tumblr user put it. I grasped that more when reading meta information on Tumblr years later after watching the show (October 2023). I didn't think of the book and season 1 as a Mystery. I usually call it a Fantasy, but I do think Fantasy Comedy is a good descriptor as well.
Like many, I took the themes to be about free will, friendship, people do good things and bad things and are basically people, people matter, the world one has is worth loving and saving, those types of things.
A big thing that changed in GO1, the first season of the show, and the end of the book is the face swap, what many call the body swap. They showed us the clues, then revealed the trick, and then we could go back and see the clues were already there. They allowed us to see the prestige. But also...don't take things at face value.
For GO2, the Final Fifteen sends up some massive red flags that things aren't right, like not just the argument, but the actual structure of the story, the directorial choices, and such. I didn't like how it ended, but I liked David Tennant as Crowley and wanted to make the best of that. I read meta information, liked some theories, found some really interesting things through trying to figure out his sideburns, and so on.
Simply put, the GO2 story repeatedly lied to its audience. There were a lot of documented continuity issues that the fandom had with the recognition these things were intentional. GO2 gave clues that further suggested...don't take things at face value.
With GO3, Michael says the Metatron used to just fiddle with things in the Book of Life, which was a theory I worked from as a starting point while not quite fitting my own theories on GO2. But if you watch after he's gone in GO3, the story still has intentional continuity issues and a nonsensical plot.
The story kept lying. Even at the South Downs cottage, there is a continuity error with Asa's right hand.
It is still going with...don't take things at face value.
Basically, GO2 and GO3 are a complex puzzle where the audience is left to figure out what happened. Parts of GO3 are contradictory to the characters and themes of the book and season 1 on purpose to challenge the audience.
The story references deception and games plenty, and it is playing games with the audience. This play is given in a very challenging way that many people find off-putting. A big part of that is because of yes, this major genre shift if you take things at face value.
I think the Aziraphale's Nightmare theory by @/vidavalor is a good, worthwhile theory, if that helps. I still don't like Good Omens 3, but I understand it better and see pieces that fit well with the idea in mind.