State-capitalism is used to describe the German Empire and the Japanese both pre and post WWII as well as contemporary China. How does China differ form those two examples and how is it similar? Does a company like Huawei have obey the Chinese 5 year plans more closely than Krupp or Mitsubishi had to obey their governments' plans? Officially Huawei is not a SOE but it operations are part of the central plan. Huawei would prefer to rely on comparative advantage and continue to import computer chips from Korea or the US but the recent Chinese 5 year plans call for increased domestic autonomy in chip production so Huawei (and others) are tasked with developing those. They get sanctioned by the US and lose business as a result, while a purely chip importing company like Lenovo gets away with no sanctions. Following the government plan did not benefit them in the short run but will bring benefit to China overall in the form of chip production that they can fully secure and a new class of high value good they can export. Whether China is a different system then non-communist run state-capitalist countries is up for debate but I would say China maintains a greater degree of control over its enterprises than Germany or Japan did.
There have been many governments in the past that used Keynesian policy including the US, and most of western Europe before the late 70s. We do not typically call those countries state-capitalist. Maybe it is fair to say all state-capitalist governments practice Keynesian policy but that is only a necessary condition not a sufficient condition for state-capitalism.
I certainly could not see austerity as a policy of a state-capitalist country though perhaps you could argue that austerity can only be enacted by state interference in the market and thus it must also be a perverse form of state-capitalism. A sort of anti-Keynesian economics.