game version 1.20.1
zenith version 1.2.3

the enchantment table stats are not displayed (while enchanting) and additionally do not seem to "see" the shelves from zenith as real shelves

additionally infusion does not seem to work either

maxed out enchanting setup as you can see from the waila...
does anyone know what is going on

That little broom thing is an item sorter that affects UI. Try disabling mod that adds that. Also, check other mods you have that modify UI, like Exordium for example.

If it was indeed item sorter causing this, you can switch to Mouse Wheelie or Mouse Tweaks

Same version as Yuuki, but I have a lot more mods. I thought it could've been the Inventory Tweaker or the Resource pack to change the look of the UI, but with those two removed, the problem remained.

Mod list can be found here: https://pastebin.com/rPTddT57

Note: iris flywheel compat is disabled, as it crashes things.

Some more context I can add that can be interesting. From a simple setup with just using seashelfs, for the first level of infusion:

If I add a normal sword, I can only access the base levels:

However! If I add normal bookshelfs around, I start to get higher level enchantments:

So, my conclusion, is that bookshelfs, other than the base game ones, are not being used to calculate the enchantment levels of items. Why would UI mods have an impact on this? It looks like something different in here. I do agree that another mod could be colliding with this, but which one then? A UI mod doesn't look like the right way, when other shelfs are working.

FYI, I decided to create a modpack with a lot less clutter, and I was able to make it work. So there is definitely some collision there, I just don't know which yet.

@MihanDeNoob I stand corrected, and you are absolutely right. In my case, it was the mod Easy Magic, that changes the enchanting table UI to have a few extra things. It seems to kill Zenith's changes. @Yuuki-Shino please check if you have this mod in your mod list, and if you do, try to remove it.

My thoughts are that UI probably only recognizes the standard enchanting tables. I do wonder if there's a tag, or something else I don't know, that could be added to the new shelfs that would allow for them to be compatible. In any case, we'd need a compatibility mod, or an update on one of the mods, to make them work together.