Always run both public and private documentation checks (#6707)

Avoiding failures like #6705

Context in #6099

## Test plan

Even though I opened the pull request, the public build was still
tested.

.github/workflows/ci.yml

@@ -409,18 +409,18 @@ jobs:
  uses: webfactory/[email protected]
  with:
  ssh-private-key: ${{ secrets.MKDOCS_INSIDERS_SSH_KEY }}
- - name: "Install Insiders dependencies"
+
+ - name: "Install dependencies (public)"
+ run: pip install -r docs/requirements.txt
+ - name: "Build docs (public)"
+ run: mkdocs build --strict -f mkdocs.public.yml
+
+ - name: "Install dependencies (insiders)"
  if: ${{ env.MKDOCS_INSIDERS_SSH_KEY_EXISTS == 'true' }}
  run: pip install -r docs/requirements-insiders.txt
- - name: "Install dependencies"
- if: ${{ env.MKDOCS_INSIDERS_SSH_KEY_EXISTS != 'true' }}
- run: pip install -r docs/requirements.txt
- - name: "Build Insiders docs"
+ - name: "Build docs (insiders)"
  if: ${{ env.MKDOCS_INSIDERS_SSH_KEY_EXISTS == 'true' }}
  run: mkdocs build --strict -f mkdocs.insiders.yml
- - name: "Build docs"
- if: ${{ env.MKDOCS_INSIDERS_SSH_KEY_EXISTS != 'true' }}
- run: mkdocs build --strict -f mkdocs.public.yml
 
  build-binary-linux:
  needs: determine_changes