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/models/user.py

@@ -24,6 +24,11 @@ class User(Base):
         ForeignKey("teams.id"),
         nullable=True
     )
+    invite_code_id: Mapped[Optional[uuid.UUID]] = mapped_column(
+        UUID(as_uuid=True),
+        ForeignKey("invite_codes.id"),
+        nullable=True
+    )
     created_at: Mapped[datetime] = mapped_column(
         DateTime(timezone=True),
         default=lambda: datetime.now(timezone.utc)