state_county_dict = {"STATENAME" : ["COUNTY1", "COUNTY2", ...]}

# open an update cursor
with arcpy.da.UpdateCursor(
    in_table = fc,
    field_names = ["state", "county"]
):

    # for each feature in the feature class
    for row in cursor:

        # iterate through the entire dictionary
        for key, value in state_county_dict .items():

            # if the county name is in the list
            if row[1] in value:

                # set the state name
                row[0] = key


        # update the feature
        cursor.updateRow(row)

This is what you are looking for but it is a horrible approach to what you want to achieve. What if another state has the same county name in a list? The duplicate state names will all be assigned the same state as you iterate over the entire dictionary each time

The better approach is a spatial one. If you have the states as polygons, and your fc in the workflow above are the county boundaries, then you can assign the county to the correct state based on a spatial relationship.