The EPA does track Class V well inventories by state and posts that information on the web at https://www.epa.gov/uic.
Unfortunately, it does not track Class V wells by subcategory. States with primary enforcement authority for the UIC program may post that information on their individual state UIC websites. EPA manages the Class V program in several states including PA, VA, NY, CA, MN, and SD. Individual EPA regional UIC programs track that information for those states.