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

turbo.json

@@ -18,6 +18,10 @@
     },
     "check": {
       "outputs": []
+    },
+    "typecheck": {
+      "dependsOn": ["^typecheck"],
+      "outputs": []
     }
   }
 }