This is actually one of those topics where unleashing my full power level would lead to rabbit holes within rabbit holes lmao. In fact, it's very similar to Lain in the regard that no matter how many times you rewatch it you'll discover new things about it. It's also a really weird blend of pretty straight forward on the surface level plot, but completely abstract and cryptic on every other front (or just down right comical sometimes).
So to keep it somewhat contained, I'll just say that the first time I watched Utena it triggered an obsession where for the next 6 months of my life the only thing I watched, was rewatching Utena (nothing else had ever, nor since, triggered autism in me as strongly). The symbolism is really weird, but just consistent enough where you know there are deeper meanings to things, but at the same time the show's creator is a known troll and he throws plenty of red herrings.
An anon on /lit/ tipped me off to esoteric/occult symbolism being a key that can help understand the show. Something I was initially skeptical of, but after doing some research into, I can say that the creator (Ikuhara) at least had surface level awareness of western esoterism, as he playfully references esoteric symbols constantly. Usually in the lyrics of the various songs that get used in the battle sequences and in the ending themes.
I think I'll leave it there. But to give a brief example of both what I'm talking about and Ikuhara's
interesting sense of humor. In the
second Ending theme of Utena, among the several occult allusions he makes, one of them is the "Embryo of Philosophy". Gibberish on the surface, unless you realize that the Egg of Philosophy is an Alchemical term referring to the
first matter of the Philosopher's Stone. It's the kind of thing that seems like complete nonsense unless you know precisely where to look. Because it's not even a direct reference to the Philosopher's Egg, but rather a playful connection. In the same song, he mentions "a single perpetual motion machine". Perpetual motion is understood as a metaphor for eternity (since the very notion of perpetual motion is contradicted by the first and second laws of thermodynamics). And the philosopher's stone (which the embryo of philosophy is playfully alluding to), is a tool which alchemically can help achieve the goal of immortality (aka perpetual motion).
Anyway, that's just me analyzing the lyrics of one song in Utena, there are many more. So I'll spare you, but hopefully that communicated the idea the Utena is a series rich in playful references.