Migrate docs build to use uv

[browniebroke]

Description

Migrate the RTD build of the template to use uv, following the official docs:

https://docs.readthedocs.io/en/latest/build-customization.html#install-dependencies-with-uv

Checklist:

• [x] I've made sure that tests are updated accordingly (especially if adding or updating a template option)
• [x] I've updated the documentation or confirm that my change doesn't require any updates

Rationale

The template deps are using uv, let's bring the docs in line with that