i am searching for a sourdough chocolate cake or other cake that uses only sourdough

But I will say that I haven't found any such recipe, yet.

Most of the sourdough cake recipes on the internet are basic butter cakes.  In other words, they rely on creaming butter and sugar together to create nuclei for bubbles that can then be inflated by gases produced by the chemical leaveners.  In such recipes, the sourdough performs two functions: supplying acid for the chemical reaction with the baking powder or baking soda, and supplying flavor. 

Keep looking.  Perhaps you'll find a cake that uses sourdough as the sole leavener. 

Paul

It's Babka! 

https://www.theperfectloaf.com/sourdough-babka/

https://www.thefreshloaf.com/node/64557/whole-grain-sourdough-coffee-cake

I know it's not chocolate, but it is the cakiest yeast/sourdough cake recipe I have come across. I haven't made it in a while, but I make it using only sourdough, and although it could probably stand to rise a bit more, I personally love dense cakes, and the texture is less babka-y and more like a chemically-leavened cake.

I was searching high and low a while ago for sourdough cake recipes, and I did not come across much. Here is one recipe which I have not tried:

https://www.rejoiceinlife.com/recipes/gingerBread.php

And you could also search for recipes for election cakes.

Okay, it's a cherry cake rather than a chocolate cake but it is leavened exclusively with sourdough.  Maybe after fiddling with it a bit you'll be able to extrapolate to a chocolate version.

You might also want to look at yeasted cakes to see whether/how they might be adapted for sourdough.

Best of luck!

Paul