I think I like the term "thickness" over "depth" here because thickness implies a sort of solidity, an ability to stand up to being held and examined, turned over and and handled. Depth can feel unapproachable (the ocean is pretty deep and it is famously challenging to explore) while something which has thickness intuitively feels like you can walk right up to it and try to learn something.

This doesn't hold for all things - I would, for example, describe a wine as having "depth" but probably not "thickness" because in the case of potables "thickness" also implies a particular sort of textural feel, but I do like the idea of a piece of art as being thick with meaning as opposed to deep. A book which is deep can be reread multiple times, but a book which has thickness just sounds like a book that can live on your bookshelf and be paged through year after year for decades, with not only the content to support it but also the sturdiness to hold up to the use.