Use uv sync & uv run in docs build

[browniebroke]

Description

The offical RTD guide was written a few months ago and I realised after merging #5438 that we can in fact simplify a bit more.

Also upstreamed these changes to RTD: readthedocs/readthedocs.org#11655

Checklist:

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

Rationale

Simpler build steps

[foarsitter]

This was the flow I expected in the first place but didn't know how to install the optional dependencies and the existence of --extras.

I would expect the --no-dev and --frozen parameters here. Dev requirements are not required and the lock file should not change.

[browniebroke]

I would expect the --no-dev and --frozen parameters here

Good point! Fixed

[foarsitter]

Forgot that we don't have dev dependencies xD

Will add some soon ;)