chore: build playground before deploying to github pages

[lukascivil]

Objective

Ensure the playground's production bundle is built before the GitHub Pages deploy step runs, so the deployed site reflects the current release instead of stale or missing build output.

What was done

• Added a Build Playground step in .github/workflows/release-and-publish.yml that runs yarn nx run-many --target=build --projects=playground immediately before the Deploy Playground to Github Pages step.
• Gated the new step with if: github.event.inputs.dry_run != 'true', mirroring the existing deploy step so dry-run executions still skip both build and deploy.

Test plan

• Trigger the release-and-publish workflow with dry_run=true and confirm the new Build Playground step is skipped along with the deploy step.
• Trigger the workflow with dry_run=false and confirm the Build Playground step runs successfully and produces the artifact consumed by the deploy step.
• Verify the GitHub Pages site is updated with the latest playground build after the run.