What do we call powers such as setting up schools establishing local government and making regulations for marriage?

Powers such as setting up schools, establishing local government, and making regulations for marriage are typically referred to as "concurrent powers" or "reserved powers," depending on the context. In the United States, these powers are generally reserved for the states, as outlined in the Tenth Amendment of the Constitution. They allow state governments to manage local affairs and implement policies that reflect the needs and values of their communities.