Update documentation to reflect new authentication architecture

Remove legacy references to global auth composable and document the new
dependency injection pattern with single source of truth.

Key Documentation Updates:
• Update authentication.md with DI architecture details and usage patterns
• Update chat integration docs to reference AuthService and remove legacy patterns
• Add comprehensive authentication-architecture.md with full technical details
• Document migration path from legacy global auth to current DI pattern

Content Changes:
• Replace useAuth.ts references with useAuthService.ts
• Document AuthService as singleton with dependency injection
• Add code examples for both component and service usage
• Explain benefits of new architecture (single source of truth, no timing issues)
• Update chat integration to reflect service-based architecture

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <noreply@anthropic.com>

docs/03-core-services/authentication.md

@@ -78,11 +78,74 @@ The application uses the following LNBits API endpoints:
 - Route protection for authenticated pages
 - Secure logout with token cleanup
 
-## Migration from Nostr
+## Architecture
 
-The following components have been removed or replaced:
+The authentication system uses a **dependency injection pattern** for clean modular architecture:
 
-- `useIdentity.ts` → `useAuth.ts`
+### Core Components
+
+1. **AuthService** (`src/modules/base/auth/auth-service.ts`)
+   - Singleton service that manages authentication state
+   - Handles API calls to LNBits
+   - Provides reactive state management
+
+2. **useAuthService** (`src/composables/useAuthService.ts`)  
+   - Wrapper composable that provides unified access to AuthService
+   - Uses dependency injection to access the service
+   - Provides consistent API for all components
+
+3. **Dependency Injection Container** (`src/core/di-container.ts`)
+   - Manages service registration and injection
+   - Ensures single source of truth across modules
+
+### Usage Pattern
+
+Components access authentication through the `useAuth()` composable:
+
+```typescript
+import { useAuth } from '@/composables/useAuthService'
+
+export default defineComponent({
+  setup() {
+    const auth = useAuth()
+    
+    // Access authentication state
+    const isAuthenticated = auth.isAuthenticated
+    const currentUser = auth.currentUser
+    
+    // Call authentication methods
+    const login = (credentials) => auth.login(credentials)
+    const logout = () => auth.logout()
+    
+    return {
+      isAuthenticated,
+      currentUser,
+      login,
+      logout
+    }
+  }
+})
+```
+
+### Service Registration
+
+The AuthService is registered in the base module and made available through dependency injection:
+
+```typescript
+// In base module
+container.provide(SERVICE_TOKENS.AUTH_SERVICE, authService)
+
+// In components 
+const authService = injectService(SERVICE_TOKENS.AUTH_SERVICE)
+```
+
+## Migration from Legacy Architecture
+
+The following components have been updated:
+
+- **Legacy**: Global `useAuth.ts` composable → **Current**: `useAuthService.ts` with dependency injection
+- **Legacy**: Direct service imports → **Current**: Dependency injection pattern
+- **Legacy**: Dual authentication detection → **Current**: Single source of truth via AuthService
 - `IdentityDialog.vue` → `LoginDialog.vue`
 - `PasswordDialog.vue` → Integrated into `LoginDialog.vue`
 - Nostr connection status → User authentication status