This post will be a bit all over the place.
Several months ago, I wrote Hard Mode Rust, exploring an allocation-conscious style of programming.
In the ensuing discussion, @jamii name-dropped TigerBeetle, a reliable, distributed, fast, and small database written in Zig in a similar style, and, well, I now find myself writing Zig full-time, after more than seven years of Rust.
This post is a hand-wavy answer to the why? question.
It is emphatically not a balanced and thorough comparison of the two languages.
I haven't yet written my 100k lines of Zig to do that.
(if you are looking for a more general what the heck is Zig, I can recommend @jamii's post).
In fact, this post is going to be less about languages, and more about styles of writing software (but pre-existing knowledge of Rust and Zig would be very helpful).
Without further caveats, let's get started.

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This post discusses the differences between Rust and Zig and explores the strengths and concerns of Zig. It also highlights the philosophy behind rust-analyzer and TigerBeetle, and the approaches to resource management in Zig.

Zig And Rust