Ok, so another pro-nuclear puff piece. Why do I say that? Because it talks about nuclear waste without ever mentioning the other kind: fuel processing waste.
Nuclear fuel needs to be enriched. Enriching is simply upping the percentage of U-235 (the rest is mostly U-238). Civilian reactors tend to have relatively low enrichment rates. So-called weapons grade is enriched to a very high percentage and requires different processes.
So U-235 and U-238 are chemically identical. So how do you enrich a sample? Centrifuges. You make a Uranium gas. The U-238 molecules will be heavier. Spin them in a centrifuge and you can extract them at a greater percentage and then pass on the gas to the next centrifuge. You do this repeatedly until you get the enrichment level you want and then extract the metal from the gas.
The gas of choice is UF6 (Uranium Hexaflouride). That itself is a toxic byproduct that needs to be stored or otherwise dealt with. We don't really have a good solution for this either. There is some reprocessing that basically turns UF6 into less toxic UF4 but it's not really economic.
As always, pro-nuclear propaganda focuses on deaths because deaths doesn't capture the negative impact of nuclear. Why? Because the Chernobyl disaster directly killed less than 100 (it also probably killed tens of thousands through cancers in the following years but that's harder to attribute and easier for people to collectively ignore).
But still the Chernobyl absolute exclusion zone, from one incident, is quite literally 1,000 square miles even now, almost 40 years later.
Deaths or deaths per TWh just doesn't capture that impact and those failure modes, which is precisely why such propaganda focuses on deaths.
But none of that is the big problem with commercial nuclear power. It's the fallibility of humans to manage, maintain, build and transport and store (fuel and waste) to a sufficient level to avoid disasters. The profit motive provides an incentive to skimp on some or all of these. Corruption is an issue with both corporations and governments.
Humans are just incredibly bad at managing long-term consequences, which is why we have the climate crisis to begin with.