What is a word for partaking in art?

Solution 1:

What about experiencing? An experience is

an event or occurrence that leaves an impression on someone

So it can describe the act of being moved by any piece of art--be it food, music, visual, or something else.

Solution 2:

Generally I think appreciate is used in this context, but without coupling it to "enjoy" since as you mention "appreciate" rather implies enjoyment already.

I want to create art that I also appreciate.

If you are determined to keep the "enjoy" in the sentence, you might say

I want to create art that I also enjoy reveling in.