Proven Forest Management Act of 2022 This bill directs the Department of Agriculture (USDA), when conducting a forest management activity on National Forest System land, to coordinate with impacted parties to increase efficiency and maximize the compatibility of management practices across such land. USDA shall conduct such an activity on National Forest System land in a manner that attains multiple ecosystem benefits, including reducing forest fuels and maintaining biological diversity. However, a forest management activity shall not be conducted if the costs associated with attaining such benefits are excessive. Additionally, the USDA shall (1) establish any post-program ground condition criteria for a ground disturbance caused by a forest management activity required by the applicable forest plan, and (2) provide for monitoring to ascertain the attainment of relevant post-program conditions. The bill categorically excludes certain forest management activities for reducing forest fuels from certain environmental impact requirements. USDA or the Department of the Interior, as appropriate, in conjunction with land adjustment programs, may enter into contracts and cooperative agreements with a qualified entity to provide for fuel reduction, erosion control, reforestation, Stream Environment Zone restoration, and similar management activities on federal lands and nonfederal lands within such programs.