Yes baked beans are processed food.
Any food that is cooked, baked or altered is a processed food.
All store bought cooked and canned beans are processed food and some baked beans and other canned beans may have other ingredients added to them to add to the flavor.
Baked beans are on that list of processed food because they are cooked and baked and altered to make the baked beans.
Any food that is cooked, baked or prepared is processed.
Even when you cook food at home or make your own homemade baked beans the baked beans and other cooked food is a processed food.