MC 1.17.1
Fabric API 0.40.1
CIT Resewn 0.7.1

Tested with these resource packs:

Kal's Expanded Armory
xali's Potions
Improved Elytras+
Elytras+ - More Elytras!

Examples:

Elytras change appearance properly when worn and dropped, but not while viewed in the inventory/on the hotbar.

Potions change appearance properly when held and dropped, but not while viewed in the inventory/on the hotbar.

Can you provide logs?

Just tested the rainbow elytra on my main pack with 112 mods and it works for me, your mod list is way to big for me to comb through.

I'll reopen the issue once the mod is found.

Log: [removed]
That's a vanilla Elytra renamed in an anvil to Rainbow, from Elytras+ - More Elytras!.

Here are also some examples from Kal's Expanded Armory:

Netherite Helmet renamed in an anvil to Netherite Crown

Netherite Helmet renamed in an anvil to Netherite Light Helmet

Yeah, there is really no way for me to know what is going on there.. The logs say that CITResewn loaded the resourcepack fine but you also have 366 mods running and one of them is probably the cause, probably some mod is doing something weird with the item renderer(the part that draws items in the inventory/hand).

The rainbow elytra is working fine on my end:

I'll need you to pinpoint the problematic mod by removing and adding them until the elytra appears

It's Eating Animation [Fabric] and they are aware of the issue.

Sorry for wasting your time.

It's no problem, thanks for informing me!