Currently, custom containers can already take a lot of appearances, but we can achieve even more with the following trick:

We can use a custom font and assign some unused characters in that font a huge texture. Such a character can be used in the display name of a custom container, and, with the right offsets, it will display a fully customizable container overlay. I have an example resourcepack for this on my Discord history.

I pinned a message in the suggestions discord channel that gives a lot of advice on how to implement this.