The Short Version
The scientific core of this claim is well-supported: high-level nuclear waste does remain radioactive for thousands of years and requires long-term isolation to protect people and the environment, consistent with Natural Resources Canada's published positions (including a December 2024 policy document). However, the claim overstates by using "continuous" monitoring — deep geological repositories are designed to be passively safe without perpetual active controls — and implies all nuclear waste categories require millennia of isolation, when low-level waste requires only centuries.