Further to your comments on sovereign immunity, the principle only applies to the Executive branch of the US Government. As an example, the Government cannot be sued unless it consents, such as the limited jurisdiction allowing suits against the Government for patent infringement. A patentee can’t obtain injunctive relief nor the same type of damages allowed against a non Government infringer, but can only obtain “reasonable ... compensation” - essentially a license fee. Nor a jury trial, and not any US District Court, only the US Court of Federal Claims.
Sovereign immunity is alive and well with the US Government with specifically carved out exceptions. But no way this extends to the private acts of Congress critters even if they try to claim it was part of their “job.”
Sovereign immunity is backed by many different directions. It is further backed by bills like the Westfall Act that even erases tort claim actions. Remember what I mentioned, please, “It does not, however block the identification of facts. It just means they cannot be sued or arrested for the act sans actual crimes.” The problem in the thread is the release of information, not self incrimination for a capital offence. That is unless he perjured himself with false statements under oath which he may have done.
A decent article on immunity is this one from Cornell University Law:
https://www.law.cornell.edu/wex/sovereign_immunity
rwood