Concerning doctor patient confidentiality in the GDR I found this essay:
To summarize:
Doctor-patient confidentiality existed and was nominally protected by law. The extent of confidentiality was more limited than in West Germany. For example doctors had no expectation of exemption of punishment if they prevented a crime and didn't report their patients intent to commit the crime.
Nonetheless official publications on medical ethics stressed the sanctity of doctor-patient confidentiality within these limits and it seems that doctors used these references to refuse to give testimony in court.
Having said that, the reality looked different. It is estimated that 5% of East German doctors worked as informants for the STASI and some must have deliberately broken their vows in doing so. It seems that historians haven't systematically sifted through all the files, so the actual extent is unknown. Given the methods the STASI employed it seems unlikely that they gave second thoughts about breaking into doctor offices and simply took/copied the documents they wanted.
To my knowledge the exact same thing can be said about client-lawyer confidentiality and confessionals. They were all legally protected but lawyers and priests/reverends were sometimes too happy in passing on information and never punished. If the STASI couldn't get the information that way they had no qualms with spying and breaking the law themselves.
Concerning legal privilege:
Attorney-client privilege existed, and it was the only legal privilege recognized under Soviet law. See RSFSR Code of Criminal Procedure, Art. 61, Art. 72. As noted by u/cavetroglodyt, doctor-patient confidentiality existed, and was recognized in law, but it did not rise to the level of legal privilege (i.e. - as a claim of confidentiality, it could be defeated by a showing of need by the adverse party).
There was no spousal privilege, no work-product privilege, and no trade secret privilege.
There was also no privilege against self-incrimination, akin to the U.S. 5th Amendment. See The Soviet Legal System and Arms Inspection: A Cast Study in Policy Implementation, p. 298.