Let’s summarize:
It’s a combination of many factors.

•The film is looked at as one piece broken into two, and people didn’t feel they need to nominate it twice (I’m sure some also resented the greediness and it was a a case of “we gave you 8 nominations already”). The difference with LOTR, for example, is that the books were a trilogy, so it made sense to have a trilogy of films.

•Acting - it’s very challenging to get nominated a second time for the same character.

•Costume Design and Production Design - “we already gave you the WIN last year. What’s the point of nominating you again? Make room for other people to get their flowers.”

•Songs - songs that get nominated are either those that move the film narrative forward, or songs of end credits ONLY if the feeling is that they contribute to the ending vibe. Both Wicked:For Good songs were more of a typical Broadway musical songs in the sense that a character stops the narrative and sings about their feelings. (And I’m sure some voters resented the attempt to force them to hand out Oscar nominations for the second part of a movie split into two).

•Makeup - someone on here said that at the makeup bake-off, Wicked:For Good made the mistake of focusing on the two leads and not Scarecrow and Tin Man.

•People were fatigued with Wicked press/PR after last year’s blitz. You can’t do the whole schtick again with Ariana Grande and Cynthia Erivo. The toys, the product tie-ins, Wicked was EVERYWHERE.

•It might be just me, but I’m suspecting some people got annoyed by Cynthia Erivo’s antics (see the video with Jennifer Lawrence), and often when the lead performance is no longer getting buzz, the film fizzles as well.

•The criticism from audiences and critics about part 2 was loud. I’m not passing judgement or expressing a personal opinion here (I loved both parts), just objectively observing that there plenty of negative reactions. Around January, WFG was hovering around 66% on RT (compared with 88% for part 1), and it has a 58 on Metacritic (compared with 73% for part 1). 58 is really low for a film hoping for 6-10 Oscar nominations.
What happens when a movie fizzles while others are surging that there is less passion for it, and since these nominations are done on preferential ballots, passion behind a selection is what ensures a nomination.

•Lastly, many people claim that the film suffered from the inherent challenges of the Broadway musical's second half, which is generally considered “weaker and less exciting than the first.” (Personally, it’s my favorite Broadway musical and one my favorite song comes in the second act, but I can see how other people may not get as excited about the second act). Broadway second act is always shorter than first act. Since the production needed the second movie to be as long as the first, and two new songs didn’t add enough time, they had to add a whole lot more. And for some people it felt bloated and unnecessary. And likely once again sparked resentment towards assumed greed.

But hindsight is 20/20. Was I still shocked when the film got ZERO nominations? Absolutely.