I'm a big fan of this show. And I say that as someone who has read just the first 3-4 books maybe (I've read summaries for probably the first 8, I had mistaken that for actually reading them before, probably in this thread, as well as knowing spoilers for basically the whole series, how certain storylines play out). I've actually just started to try to read the books again, finished book 1 and about 60% through book 2.
For the show, the second season just blows the first season out of the water. The first book really does feel out of place though, it just feels like Jordan almost wrote it as a one off, but then decided to expand it out only after writing it. I cannot say if that's actually what happened, but when I read these books years and years ago that's how I felt about it. It makes for an awkward transition to screen. The show also struggled with COVID and a certain actor straight up quiting on them when they resumed production. The disappointing ending to Season 1 and the massive book changes in Season 2 is largely a result of that actor quiting as they had to rethink the entire gameplan. You could tell it really effected the end of Season 1 which really left a bitter taste in people's mouths.
As mentioned above this show does not seemingly catch a break because then Season 2 debuts during a writers and actors strike limiting press they can do to promote it. Even then it felt like Amazon did drop the ball on even stuff they could have done. Promotion for S1 was everywhere, felt very lacking this time around. But you could tell that despite the changes made necessary by the actor quiting in S1, with the time and effort they put into the storylines and completely changed ideas and arcs of season 2 that it is starting to come together. It was much improved on S1 and much like in the books, in S2/Book 2 is where the world and characters really start to come into focus.
I think Amazon is hoping for a Game of Thrones like development. GOT had massive promo's for S1 when it released, but it didn't catch on all that much early on. Rating steadily climbed across the first few seasons though that it eventually become the cultural zeitgeist it become. While I don't think this will ever come even slightly close to taking over on that level, the improved audience scores and critics scores of S2 has it trending upwards.
I do remember the start of book 3 being super annoying, where after the big "Dragon Reborn is Back Baby" announcement they spend the start of the next book like hiding the in mountains or something I just kept thinking "DO SOMETHING". So I think they are taking the best approach to season 3 by combining book 3 and book 4 together essentially. With 14 books there's plenty of material so it's almost going to be the opposite of GOT going forward where GOT had to venture into unexplored territory as the books weren't finished, whereas here they are going to have to start condensing the books as they will never get 14 seasons to play it out a book for each season.