feat: add public homepage with Auth Engine session controls

[vib-tools]

Summary

• Add the public ygit.net homepage UI.
• Serve homepage, privacy, terms, robots, and sitemap resources from FastAPI.
• Integrate login with /api/v1/auth/login?next=/dashboard.
• Detect the authenticated session through /api/v1/me.
• Integrate logout through POST /api/v1/auth/logout.
• Keep authentication state server-side through the existing Auth Engine.

Validation

• Targeted Ruff check on changed Python files: passed.
• Ruff format check on changed Python files: passed.
• AST equivalence for backend/app/main.py: passed.
• Focused homepage contract tests: passed.
• Full pytest suite: passed.
• Smoke test with --skip-db: passed.
• Release gate with --skip-db: passed.
• Exact current head commit: 9a5ef28.

Safety boundaries

• No merge performed.
• No branch deletion performed.
• No Coolify configuration change.
• No redeploy or restart.
• No database, volume, secret, or provider operation.