Add base-demo CI validation

[codeforester]

Summary

Add CI validation for the base-demo repository so the interactive walkthrough does not drift or break silently.

Scope

• Add a GitHub Actions workflow in base-demo.
• Install only lightweight prerequisites needed for demo validation.
• Run BATS tests for shell scripts.
• Run the demo in --non-interactive mode.
• Verify basectl check base-demo, basectl doctor base-demo, and basectl test base-demo where feasible.

Acceptance Criteria

• Pull requests to base-demo validate the demo script and support scripts.
• The CI workflow is simple enough for a demo repo and does not take excessive time.
• The validation catches missing executable bits, missing env contract behavior, and broken demo steps.

Source design: docs/base-demo-spec.md.

[codeforester]

Closing as resolved by codeforester/base-demo#2, which landed the base-demo CI validation workflow on the base-demo default branch.