Our federal government is one of limited, enumerated powers. The Constitution lays out the powers the federal government has, and notes that all other rights and powers are reserved to the states, or to the people. To add a power to the federal government that the Constitution doesn’t already grant requires an amendment to the Constitution.
If a treaty made by the federal government could trump state law on any and every subject, then we have the curious contradiction that the federal government could grant itself any power merely by including the language in a treaty.
That’s not how it works. A treaty may only reflect Congress’ powers. It may not exceed the powers of the federal government.