Black Hills Forest Protection and Jobs Preservation Act of 2022 This bill provides for vegetation management projects and timber production projects on certain National Forest System lands in Montana, South Dakota, and Wyoming. The bill directs the Forest Service to issue one or more decisions using expedited authorities for compliance with environmental review requirements to carry out vegetation management projects on land in the Black Hills National Forest. Furthermore, the Forest Service shall categorize the Black Hills National Forest and the Bighorn National Forest as being very high priority for ecological restoration that involves vegetation removal. The Forest Service must also use specified amounts made available for forest thinning and timber harvesting for timber production in the Bighorn National Forest, the Custer Gallatin National Forest, and the Black Hills National Forest. In carrying out such timber production, the Forest Service shall use, to the extent practicable, the categorical exclusion for certain forest management activities and specified emergency action authority. A vegetation management or timber production project carried out under this bill shall not be subject to judicial review. Such a project may not be carried out on (1) a component of the National Wilderness Preservation System, or (2) an inventoried roadless area.