there's too much symbolism to get into all of it here, but i'll go over some of the big ones. most symbols have multiple meanings or interpretations, but i'll stick to the main ones.
- flowers are a huge deal, specifically roses. in duels there's the obvious metaphor for penetrative sex, and all the baggage that carries. when they show up in the corner or as part of a frame they usually are associated color wise with one of the characters in that scene, often to indicate that they're being Main Character-y for lack of a better term. flirting, looking cool, making an entrance. obviously not universal, but that's a rule of thumb that i'm pretty sure is accurate most of the time. outside that, colors are generally meant to represent things associated with the character of that color. for example, if there's a lot of orange on screen there's probably some unrequited love going on even if juri isn't around.
- cars, and other methods of tranportation. represent masculinity and adulthood, as well as sex and other things that are commonly linked similarly in modern culture and in fiction. you make out in your car before you have your first time which makes you a man, etc. i wrote something previously somewhere about the car symbolism but i can't find it. but basically what i had to say was the car represents the impossible standards of toxic masculinity as made obvious in the scenes with touga. he's inviting others to ride in the car, because he's the pinnacle of masculinity among the students, as is clear from him winning against utena in the first arc. he's what saionji and to a lesser extent all the other characters want to be, he's student council president and is the most powerful character. but he can't actually live up to all that, so when he has to make his own moves without akio's support he instead has a much lamer bike with a sidecar. theres a lot more you could read into that re: his relationship with saionji, but i'll cut this short here.
- cars aren't entirely negative though. they also represent freedom, as made clear in the movie, though i won't go farther since you didn't say if you'd seen that.
- touga's carrot represents his penis (bet that one slipped by you. it's super subtle and you need a massive brain to understand what him posing like that means)
- coffins represent being trapped within your fear of death, or just being trapped in htori where you'll never age. lots of things around ohtori are shaped like coffins, or in ways that the camera can frame them as coffin shaped. you can only break out of your coffin by accepting that going into the painful unknown is better than staying behind, which is what happens to anthy in the last episode. utena breaks through the coffin and anthy realizes that the real world is worth living in and is finally able to leave akio, and therefore ohtori academy
- the animals represent the fact that it's funny when animals do things you wouldn't normally expect them to. i'll go into more detail on this when discussing nanami, where i'll break down the meanings of her comedy episodes.
- other symbols i can't get into include gardens, the statues, chuchu, and the hair styling choices of the character designers.
i'll stop here for this post and continue with an explanaation of mikage (which will hopefully be shorter!)