I'd sure want to be very careful with health-risk assessments. But nickel-63 is pretty low-energy. According to this fact sheet absorbed radiation from exposure to skin is negligible without shielding. And that level of radiation is easy to shield so the battery casing presumably blocks all of it. (Tbf I believe fact sheets like that assume that your dead layer of surface skin cells has a small shielding effect, so the calculation is different if it gets in your body.)
The article also mentioned a possible variation with strontium-90 which is stronger stuff. It's emissions are 8 times more energetic than Ni-63, and instead of decaying to stable copper, strontium-90 decays to yttrium-90 which emits radiation several times again more energetic than strontium-90. Here's another fact sheet. (Sorry about using two different sources for fact sheets. I had a hard time finding one source with facts on both isotopes.)
The term "radioactive waste" suggests products from uranium fission, and the isotopes they decay to which can have extremely high-energy emissions, and decay through chains of several radioactive isotopes before finally decaying to stable elements which means extremely long half-lives overall. IMO the comparison is misleading. It's kinda like comparing one "moderate" air quality day to many days inside a smoke stack.
With the exception of the listed medical devices, all the other use cases point to military, and it would make sense to have such a battery in that environment.
Medical devices definitely make me ask your question.
But nothing actually new, just downscaled. This was possible before, but not done because we don't want to give people the ability to get radioactive material, even in small quantities.
Ok so maybe my calculation is off, but based on the specs in the article the battery on my phone would become 225x225x5 mm in size to be equivalent on the LiPo it currently has.
That seems way too big to be usable, and contrary to what the article says about this battery being more energy dense...
(Calculation is - 4385mAh x 5V = 21925mWh, so around 220 batteries as they output 100mW, and as they are 15x15x5 it becomes ✓220*15=~225 so 225x225x5)
It's more energy dense because it carries 50 years of power within it. It's not a rechargeable battery. They're discussing the energy density, you're measuring the energy output per cubic mm per second.
That said, this reads like a fluff piece so I wouldn't overthink it.