Can the federal government directly modify state law?
The U.S. Supreme Court has limited the authority of Congress to directly regulate the operations of state governments. This is called the anti-commandeering doctrine.
It is articulated in U.S. Supreme Court cases like New York v. United States, 505 U.S. 144 (1992), which held that the Low-Level Radioactive Waste Policy Amendments Act of 1985, which, among other things, imposed upon states the obligation to provide for the disposal of waste generated within their borders, unconstitutionally commandeered states to enact legislation that the federal government directed it to enact.
Congress can pass federal laws that pre-empt, which is to say, nullify or invalidate, state and local laws, and it can give states an incentive to modify state laws, but it cannot actually modify state laws directly, itself.
The U.S. government can also directly modify the laws of the District of Columbia, Puerto Rico, or other self-governing territories because all of them are not part of U.S. states. This authority over areas outside of U.S. states which is granted to Congress under Section 8 of Article I to the U.S. Constitution, and is limited primarily by Section 2 of the Twenty-First Amendment, which arguably forbids Congress from modifying the the alcohol laws and regulations of these self-governing possessions of the United States which are not parts of U.S. states.