Refactor authentication architecture to eliminate dual auth complexity

This major refactor consolidates the authentication system to use a single
source of truth, eliminating timing issues and architectural complexity
that was causing chat and payment functionality problems.

Key Changes:
• Remove old global useAuth composable and replace with useAuthService wrapper
• Update all 25+ files to use consistent auth pattern via dependency injection
• Eliminate dual auth detection workarounds from services (ChatService, PaymentService, etc.)
• Fix TypeScript errors and add proper Uint8Array conversion for Nostr private keys
• Consolidate auth state management to AuthService as single source of truth

Benefits:
• Resolves chat peer loading and message subscription timing issues
• Fixes wallet detection problems for Lightning payments
• Eliminates race conditions between global and injected auth
• Maintains API compatibility while improving architecture
• Reduces code complexity and improves maintainability

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

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

src/pages/LoginDemo.vue

@@ -187,7 +187,7 @@ import { Card, CardContent } from '@/components/ui/card'
 import { Button } from '@/components/ui/button'
 import { Input } from '@/components/ui/input'
 import { Label } from '@/components/ui/label'
-import { auth } from '@/composables/useAuth'
+import { auth } from '@/composables/useAuthService'
 import { useDemoAccountGenerator } from '@/composables/useDemoAccountGenerator'
 import { toast } from 'vue-sonner'