Is it worth running uv inside a docker container?

Sometimes, yes, but I would say it depends a lot on your base image and project. If nothing else, it gives you a runtime environment that is identical to your development environment.

Using uv at build time can dramatically reduce your build times if you properly handle the uv cache. https://docs.astral.sh/uv/guides/integration/docker/#caching

It's also easy:

COPY --from=ghcr.io/astral-sh/uv:latest /uv /uvx /bin/

https://docs.astral.sh/uv/guides/integration/docker

If you are using it for your project, wouldn't you necessarily have to use it for your Docker setup as well?