chore(github): Add manual trigger for building docs

[Savio-Sou]

Description

Problem*

Further to #3349, part of our docs are now automatically generated instead of manually written.

At times we might want the flexibility to trigger a doc build manually to e.g. gather such generated docs (in addition to building docs along Noir pre-releases), but we currently don't have the option.

Summary*

This PR adds the ability to manually run the "Build docs" action.

Additional Context

Reference: Manually running a workflow | GitHub Docs

Demo: https://github.com/noir-lang-test/noir/actions/workflows/build-docs.yml

The demo workflow failed as actions are not properly set up in the test repo, but with this PR merged we will get the same "Run workflow" button.

Documentation*

Check one:

• No documentation needed.
• Documentation included in this PR.
• [Exceptional Case] Documentation to be submitted in a separate PR.

PR Checklist*

• I have tested the changes locally.
• I have formatted the changes with Prettier and/or cargo fmt on default settings.

[Savio-Sou]

Oh hmm didn't realize the action does PR-specific checks, so manually triggering it doesn't really work without further modifications on the workflow 😅

[Savio-Sou]

Stupid me, Publish Docs rather than Build docs should actually be used for manually publishing new docs.

Creating a PR to revert this PR.