I have a reasonable understanding of batteries, but my understanding of the details of DC-DC converters is small at best.
I was looking at some Youtube videos about these batteries and in one, the host was complaining about poor shelf life of the charged batteries. He also complained about batteries that died and couldn't be recharged. Part of that could be poor quality parts and/or assembly, but part is due to the design constraints. Low idle current (as you stated), operating current range of microamps to amps, very small size, and of course, very low price all add up to a challenging design. There might not be a part that is suitable. It might exist, but doesn't have a published datasheet because it's only available in quantities of 10,000 or more. It might even be a custom or semi-custom chip.
These things are relatively new on the market. It'll take some time before everyone decides if the idea is practical and cost-effective. Welcome to the bleeding edge!
Ed