No, aloSIM does not provide an unlimited data eSIM for Vatican City. All of the Vatican City plans listed by aloSIM have a fixed data cap, with the largest offering 20GB for 30 days at $33.00 USD, a 10GB plan for $24.00 USD, and a 5GB plan for $14.50 USD. Each of these plans is valid for 30 days and uses 5G connectivity.
Choosing a fixed data plan can be more cost‑effective for most travelers, unless you are an extremely heavy data user who would benefit from a truly unlimited option.