Add invite code registration system for beta

Backend:
- Add InviteCode model with single-use codes
- Add invite API endpoints (create, list, revoke, validate)
- Modify registration to require invite code when enabled
- Add REQUIRE_INVITE_CODE config toggle (default: true)
- Add Alembic migration for invite_codes table

Frontend:
- Add invite code field to registration page
- Validate invite code on blur with visual feedback
- Pass invite code to registration API

Admins can generate invite codes via /api/docs (Swagger UI).

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

backend/app/core/config.py

@@ -38,6 +38,9 @@ class Settings(BaseSettings):
     # Security
     BCRYPT_ROUNDS: int = 12
 
+    # Registration
+    REQUIRE_INVITE_CODE: bool = True  # Set to False to allow open registration
+
     # CORS - set FRONTEND_URL in production (e.g., https://patherly.up.railway.app)
     CORS_ORIGINS: list[str] = ["http://localhost:3000", "http://localhost:5173", "http://localhost:5174"]
     FRONTEND_URL: Optional[str] = None