Did I accidentally make cheese? I was making a bran muffin recipe that called for 3/4 c buttermilk, which I didn't have. I took 3/4 c fat-free milk and added 2 tsp white vinegar and let it sit. I added  1 tsp vanilla.

Since I was going to use coconut oil and thus needed the "buttermilk" to be slightly warmer than room temperature (so the oil wouldn't harden), I put the "buttermilk" in the microwave for 30 seconds. The photo shows the unwanted result - I guess the milk separated from the whey and formed this glob. Can I assume this is unusable? I'd like to understand better what happened.
Yes, you did; although in a non-traditional manner :)  You created an acid-set cheese.  These are made by adding an acid (e.g., lemon juice or vinegar) after heating the milk (e.g., paneer) or by heating soured (acidified) milk (e.g., quark).

It appears that your microwave blast caused the proteins to combine into a single clump.  Normally, the heat is more gently applied.  From your picture, it seems to be most similar in texture to the curds used in a poutine.

Let us know how it tastes!