Does sovereignty refer to the supreme absolute power of a state within its own territory?

Yes, that is the definition of sovereignty. When applied to a nation or country, it implies absolute authority over its lands and citizens, subject to its own laws and restrictions. In the US, the individual states under the Constitution are subject to the mandates of that document regarding the rights of individuals, and regarding the powers it grants to the Federal government. "State sovereignty" is a legal principle that US states are acknowledged by the Constitution to have control over the laws and activities within their jurisdictions. This is subject to restriction in some cases by the Congress under Article 1, Section 8 of the Constitution, to prevent individual states from discrimination in interstate commerce.