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/api/router.py

@@ -1,8 +1,9 @@
 from fastapi import APIRouter
-from app.api.endpoints import auth, trees, sessions
+from app.api.endpoints import auth, trees, sessions, invite
 
 api_router = APIRouter()
 
 api_router.include_router(auth.router)
 api_router.include_router(trees.router)
 api_router.include_router(sessions.router)
+api_router.include_router(invite.router)