Butter is milk fat. Buttermilk is where the protein goes. Churning cream is a separation process.
Butter isn't pure churned cream. It's the fat churned or separated out of cream, leaving behind buttermilk (or, rather, the butter is what is left behind, if you are pouring out the buttermilk after churning).
There is some protein in butter still left, but probably less than a gram if it isn't shown in the nutrition facts. Butter is closer to pure fat (especially if it's clarified like ghee, which is used in South Asian cuisine) than related dairy products like heavy cream. Butter is 80% fat or more, heavy cream is around 30 to 40%, and buttermilk is around 2%.
If you want what is basically the opposite of butter, a dairy product high in protein but low in fat, that's what whey is for. Whey is separated out during cheese making and is pure protein when extracted commercially to make powder (whey protein isolate). Whole milk and buttermilk are what you want if you need the carbohydrates (sugars), though it's all simple carb (lactose). Whole milk has a better balance of macronutrients than any of the dairy byproducts, if that's what you need.