circular reasoning is a potential source of unsoundness

I think the right way to think about it is not that circular reasoning, or impredicativity is a source of unsoundness, but that predicativity is just a really powerful tool to constrain logics so they don't accidentally become unsound.

Just like it's absurdly easy for a programming language to accidentally become Turing-complete, it's absurdly easy for a logic to accidentally become unsound. But I don't think that impredicativity is the source of the unsoundness. There's impredicative logics like say, second order arithmetic that are sound. There's probably whole worlds of them nobody has thought about yet. But it's easier to think about soundness and prove it for predicative logics.