No, that’s not true. The concept of Westphalian sovereignty was laid down and (somewhat) universally applied after the Peace of Westphalia. But there were plenty of states before that. The doctrine of Westphalian sovereignty amounts to nothing more than a statement that “each state should mind its own business”.
By your definition, most of medieval Europe and imperial China were not states. The Roman Empire and the Roman Republic were not states, nor the Greek city-states, nor the Sumerian ones, nor Ancient Egypt, and many more. Even a cursory look at human history is incompatible with the notion that the concept of a state materialised after the Peace of Westphalia.
No, they were not.
They were forms of government that had important difference with what a state is. The monopoly in the use of force, for giving just one. To have a government force is not the same as to have a state that have monopoly of force in a land, that includes one.or.more nation and that is independent of the people that are part of the government class (as in group of people, not as in Marx/Weber concepts), that is why they are treated different and political science start studying state as it is from a westfalian order perspective and not from before that. Whit this I’m not saying there wasn’t state like orders, but it wasn’t state, in the same.way as atenean democracy was not a democracy as we understand it (for the Greeks, democracy was a perversion , actually)