I don't think Zig is going to be better than Rust at preventing other bugs. I don't know. No one knows. Software correctness is a very tricky thing about which we don't know much more than we know. UB are a cause of many bugs, and Zig eliminates many kinds of UB; Rust eliminates more. But Zig is also better at things we also know reduce bugs: simple semantics with simpler analysability, and shorter turnaround, which means more tests. In formal methods research we also have an analogous choice of approaches: more soundness at the cost of higher complexity and effort or vice-versa. There is no point hypothesising about which works better because even the experts have no idea, and it's certainly possible they are about even. The only thing that can settle this is empirical research.
Again, you misunderstand. Both Zig and Rust have much less UB than C. The delta between Rust and Zig comes at a cost to language simplicity and to more testing. You're guessing that that cost's negative impact on correctness is smaller than that positive delta. It's a reasonable guess, but so is the opposite one, and neither is more proven than the other, which would be my guess (while I don't write safety-critical code these days, I worked on safety-critical realtime software where a bug or even a later response could cost the lives of many people; in such correctness-critical domains C is preferred over C++ despite being less safe), although I would even more confidently bet that the real difference, whichever way, is small.
