Yeah, it's tough to get the combo of all of those things, for other reasons too. I would probably want to first reach for VS: Code, which uses ripgrep for search. But that's a "important component written in Rust", rather than a whole-Rust project. There's tons of tools like ripgrep, which is the most well-known, but it's hard to say how popular they are. And there are things like 1password, which do run on people's machines, but aren't open source.
I actually have recently seen a bug report that implies something really, really huge in this space, but I don't want to jinx it, so I'm not gonna link just yet. We'll see :)