I am a bit suspicious about the choice of startup time as the metric to evaluate performance in Claude Code. With a rewrite from a language like Zig to Rust, my biggest performance concern would be allocation. Where a Zig app might use a fast linear or buddy allocator, a Rust app is more likely to use malloc. During startup, both versions are likely to make tons of allocations. In fact, the Zig version is likely to make larger allocations during startup to reserve memory for its custom allocators. So I would expect both versions to be roughly on par, or Zig slightly worse there. However, during normal execution, I would expect the Zig version to be potentially faster, because it has paid the cost of malloc at startup and now an allocation might be as fast as incrementing an integer. This is speculation, but I would like to see performance numbers for the rest of the app lifecycle.
Those were in the article https://bun.com/blog/bun-in-rust#2-5-faster