Complete Story 1-1 and fix TypeScript issues

Add TypeScript strict mode and typecheck tasks to monorepo infrastructure.
Fix E2E test @payload-config alias and frontend TypeScript errors.

- Add tsconfig.json to backend with strict mode and path aliases
- Add typecheck task to Turborepo and all packages
- Fix @payload-config alias for E2E tests and dev server
- Add setToken method to AuthService for middleware use
- Fix implicit any types in Footer.astro and Header.astro
- Remove invalid typescript config from astro.config.mjs

apps/frontend/tsconfig.json

@@ -5,5 +5,6 @@
     "paths": {
       "@shared/*": ["../packages/shared/src/*"]
     }
-  }
+  },
+  "exclude": ["node_modules", "dist", "tests"]
 }