This word was new to me, but looking it up I wanted to say "Yes" but have since changed to "no". Definition:
Suzerainty (American accent: soo-zer-en-tee) happens when a country X has its own government but cannot act independently because of a more powerful country Y. This more powerful country Y is called the suzerain and can usually control the foreign relations of X (how X interacts with other countries).
When it comes to foreign policy in the US, it is mostly handled at the federal level. States are more likely to strike deals with foreign companies than foreign governments. OTOH the federal government is not equivalent to a distinct country and is made up of representatives from the states.
One thing I don't like about the US system is that all our representatives spend a huge amount of time in Washington D.C., away from the people they "represent". And then the lobbyists have a single destination to convince a lot of people to support their stuff. It might be better if they all stayed in their home states and handled congressing electronically on zoom or something.
Lobbyists can easily create big zoom meetings that still get everyone virtually in one spot.