...and FISA generally operates under the supervision of the Chief Justice of the USSC(?)
No. FISA is a part time gig for already-appointed federal judges. CJ role is to name the judges who will get that assignment. Other than that, it's hands off. FISA court system has its own appeals court.
The whole thing is a boondoggle sham on the public.
“FISA/FISC generally operates under the supervision of the Chief Justice of the USSC(?)
https://epic.org/privacy/surveillance/fisa/fisc/
Electronic Privacy Information CenterDefend Privacy.
The Foreign Intelligence Surveillance Court (FISC) was established by Congress in the Foreign Intelligence Surveillance Act (FISA) of 1978. The role of the FISC is to provide judicial oversight of Intelligence Community activities in a classified setting. The FISC is composed of federal judges appointed by the Chief Justice of the U.S. Supreme Court, and its decisions can be reviewed by the Foreign Intelligence Surveillance Court of Review (FISCR) and the Supreme Court.
After the FISA Amendments Act of 2008, the FISC has to rule on important and novel Fourth Amendment issues raised by the government’s proposed targeting and minimization procedures. Most of the FISC’s orders and filings are highly classified, but, after the USA Freedom Act, any significant legal interpretations by the court must be made public.
https://epic.org/privacy/surveillance/fisa/fisc/