Using multithreading in bgworker is possible if you do not use any Postgres runtime inside thread procedures or do it in exclusive critical section. It is not so convenient but possible. The most difficult thing from my point of view is error reporting.
Happy to be proved wrong, but I don't think this is correct.
PostgreSQL can call sigprocmask() in your BGWorker whenever it wants, and "The use of sigprocmask() is unspecified in a multithreaded process" [1]
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