For me it means I can fork the repo and start hacking on the code immediately, and it will have reasonable quality.
With C++/Python and even Node I often find myself wasting half a day just getting it to build.
When I see a CLI tool written in Rust or Go, it usually just works out of the box without having to mess around with godawful pip environments or conda.
"Written in Rust" carries with it significant promises that only Go also has. (Go has a lot of the same promises, for having good tooling and the same mostly-statically-compiled philosophy.)
"Written in Rust" tells me a project is easy to install and easy to hack on. I am far less interested in using non-Rust projects, and I am definitely disinterested in making code contributions to non-Rust projects.
Case in point: It took me much longer to write this comment than it took to install and use marmite.