The benefit of a rust rewrite is memory safety improvements, but currently they've just rewritten zig to unsafe rust so they don't have that either yet
You wouldn't notice either of those if you were a user, unless you happened to hit one of those bugs.
The latest Claude installer (2.1.215) possibly does not have it anymore https://github.com/anthropics/claude-code/issues/4953#issuec..., but more tries on various machines are needed to confirm that.