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/schemas/invite_code.py

@@ -0,0 +1,34 @@
+from datetime import datetime
+from typing import Optional
+from uuid import UUID
+from pydantic import BaseModel, Field
+
+
+class InviteCodeCreate(BaseModel):
+    """Schema for creating a new invite code."""
+    expires_at: Optional[datetime] = Field(None, description="Optional expiration time")
+    note: Optional[str] = Field(None, max_length=255, description="Note about who this code is for")
+
+
+class InviteCodeResponse(BaseModel):
+    """Schema for invite code response."""
+    id: UUID
+    code: str
+    created_by_id: UUID
+    used_by_id: Optional[UUID] = None
+    expires_at: Optional[datetime] = None
+    note: Optional[str] = None
+    created_at: datetime
+    used_at: Optional[datetime] = None
+    is_used: bool
+    is_expired: bool
+    is_valid: bool
+
+    class Config:
+        from_attributes = True
+
+
+class InviteCodeValidation(BaseModel):
+    """Schema for invite code validation response."""
+    valid: bool
+    message: str