So when the entire style of government and bureaucracy is dissolved you think the country continues?
Yes, normally as long as there is legal continuity, countries retain their identity through changes of systems of government.
For example today’s Germany is generally considered to be the same country as the North German confederation founded in the 19th century.
Likewise the end of communism in Eastern Europe didn’t cause Bulgaria, Poland, or Hungary to cease existing, just change their form of government.
https://xkcd.com/810/ was oddly prophetic