In a project like PostgreSQL, those scars are reflected in unit tests demonstrating that they’re fixed. It’d be hard to pass its test suite and not be as robust as the original.
This is not true, even in principle, even for Postgres itself. You'd be right to say that it'd be hard to pass the test suite and not be robust at all to some extent. But even in Postgres, I bet that you can quite easily introduce a change that will pass the whole test suite but reduce robustness compared to the latest release (for a somewhat silly example, add a call to `exit()` on a timer that's longer than the longest duration test in the suite - that will significantly reduce robustness while still passing the entire test suite).
So no, I wouldn't judge a rewrite as being equal just because it passes the tests. That said, I don't think that means you shouldn't do it. You just have to be pragmatic about it.
I'm not at ease regarding LLM generated code changes to a project with a (hopefully) long expected life time, but LLM generated regression tests should be less contentious. I wouldn't expect them to be maintained much; rather, if they don't perform as intended against a future build, just have them recreated.
Even a 100% test coversge is far away from verifying all behaviour.
"Program testing can be used to show the presence of bugs, but never to show their absence!"