So which should I use for a new project, as of July 2024?

Rye is perfectly fine to use as of now. It uses uv under the hood anyway, but has some niceties of its own.

For example?

Poetry.

I would.

I would use Uv - if you can handle that it's a moving target right now. (uv python, uv lock, uv sync and so on, and in pyproject tool.uv.sources). All preview features that replace similar Rye features with a more robust implementation.