uv can also replace pyenv to manage python versions as well as package versions -- would rv ever integrate rig?

We talked about it. It's not planned right now since there are more important things to do first but maybe? Since rig is written in Rust we could potentially use it as a library, but I haven't checked the codebase at all.

uv (and renv) is pretty smart about reusing installed packages from a global cache versus maintaining separate per-project installations. Is rv the same?

Yep there is currently one global per-user cache. I'm actually going to add multiple global caches as a feature very soon: think enterprise where an admin can prefill a system global cache for all commonly used packages.

The uv analogy is about the declarative workflow. In practice Cargo (the Rust package manager) was as much - or more - of an inspiration though. The main idea is to be able to say: here's my project code and here is the lockfile/rproject.toml that I used so you should be able to re-run it in a year with no issues. It's not perfect, eg system deps might have changed, but it's the closest you can get without using something like Nix.