Personally I find it rather hard to find certain decor items in the menu where you can equip decors to your lions, especially if you've amassed a certain amount of decor items/explore junk. It can often take me several minutes to find a certain items just because there's just so much stuff, even with the knowledge that it's sorted alphabetically.
Said menu having a search bar allowing you to look for specific items via keyword would make it a lot easier to find certain things.
I get you can just look for items using the search bar in your hoard, yet you have no preview of what it will look like on your lion and if you end up not liking it the item would've lost a use for essentially no reason.

Correct me if I'm wrong since I'm not too savvy with site coding, but I think a search bar wouldn't be too hard to implement into the decor equipper.