Very little --- I'll go ahead and say, to a first approximation, none --- of that safety has anything to do with software security. The same kinds of bugs that hit Java programs hit Rust programs, with maybe the sole exception of deserialization (which has nothing to do with error handling or type safety).

That matters because that's the kind of "safety" we're talking about when we discuss externalities for end-users --- not servers that need extra monitoring because they might crash.