Is it forbidden to benefit from milk and meat being mixed together in a compost, for example, or is it okay to benefit since the meat and milk were not cooked together?
Your title and question are 2 separate halachic questions.
1. Title: Mixing milk and meat in a compost bin
Or: "May I put both meat and milk products into the compost heap in close proximity?"
Cooking meat and milk together is forbidden, even if the aim is not to eat the result. See here for a discussion about cooking meat & milk to make medicine. Since it's for life-saving purposes they try find loopholes, but otherwise it's clearly forbidden.
One would have to ask one's LOR if the creation of a compost heap is considered cooking and how close the meat & milk have to be in the heap to be forbidden. Since there's no liquid involved, (except when & if you water the heap), it's not necessarily considered "cooking together" even if they are in the same heap.
Another issue would be: One you have a heap with meat & milk in close proximity, may you add more stuff to the heap, which will create more heat.
2. Question: Is it forbidden to benefit from milk and meat being mixed together in a compost
Or: "Once I have compost made from a mixture of meat & milk, may I use it?"
This is discussed incidentally at this location (חבל נחלתו י"א מ"ב) and here and they conclude that once a forbidden item (e.g. meat & milk cooked together) is rotten to the point that even a dog wouldn't eat it, then one may benefit from it.
A compost bin - when done right - can get quite hot - 49-77 degrees Celsius (120-170 degrees Fahrenheit). That's yad soledes bo right there, and would be cooking.
(That said, the compost experts advise not putting any animal products other than egg shells into your compost bin, because they tend to attract unwanted pests, including rodents.)