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/src/services/auth.ts

@@ -61,6 +61,7 @@ export class AuthService {
   }
 
   async logout(): Promise<void> {
+    const tokenForRequest = this.token;
     this.token = null;
     if (typeof window !== 'undefined') {
       localStorage.removeItem('payload-token');
@@ -68,17 +69,25 @@ export class AuthService {
 
     // Optional: Call logout endpoint
     try {
+      const headers: Record<string, string> = {
+        'Content-Type': 'application/json',
+      };
+      if (tokenForRequest) {
+        headers['Authorization'] = `Bearer ${tokenForRequest}`;
+      }
       await fetch(`${PAYLOAD_URL}/api/users/logout`, {
         method: 'POST',
-        headers: {
-          ...(this.token && { 'Authorization': `Bearer ${this.token}` }),
-        },
+        headers,
       });
     } catch (error) {
       // Ignore logout errors
     }
   }
 
+  setToken(token: string): void {
+    this.token = token;
+  }
+
   async getCurrentUser(): Promise<User | null> {
     if (!this.token) return null;