Add an action for building the docs

The docs are built on RTD, so we don't really require a separate check that ensures the docs build correctly - but not everybody has PR reviews enabled.

Also, our first check is currently the spelling check, which builds the docs before checking. With https://github.com/canonical/sphinx-docs-starter-pack/pull/240, we can run the spelling check on existing output, so splitting the spelling check into building + checking the spelling of the existing output should not increase the build times, but make it clearer what is happening.

Start by locating the existing spelling-check workflow in this repository and read the referenced sphinx-docs-starter-pack PR. Separate the documentation build from spelling validation against existing output, then confirm the workflow still avoids increasing build time and clearly reports each check.

Written by the indexing model from the issue text.