Zig doesn't promise language or stdlib stability yet, but in reality the changes are quite manageable. And it's already good enough for some high-profile real-world projects like Bun (https://bun.sh/), Tigerbeetle (https://tigerbeetle.com/) or Ghostty (https://ghostty.org/).
In the end, language stability isn't as important as it used to be, people are quite used to fixing their code when upgrading dependencies to a new major version for instance.
It remains to be seen if any of those projects will be around in a couple of years.
I haven't yet seen something that would make me have to consider Zig, regardless of my personal opinion, like other languages that have grown to become unavoidable.
In the end, language stability isn't as important as it used to be, people are quite used to fixing their code when upgrading dependencies to a new major version for instance.