You can find a lot of BS with huge supercapacitors and people's attempts to cram them into UPS and such - where replacing lead-acid battery with a LiFePO4 one would be more compact, store much more energy and even cost cheaper than supercap bs.

But what about small batteries?
I know that Lenovo implemented this in their small silo'd styluses that need just a few seconds to work for a hour or two. I can't find schematics or anything similar but I don't want to break mine to see how they did it...
All I can find is crap like this: https://youtu.be/7lzK04SD5Z4 But that's terrible: supercapacitors are typically 2.7V or 3V, you would have to charge them to 1.5V - and then it's a linear discharge to about 1.1V at which point the device would stop working. Clearly, a buck/boost circuit providing stable 1.5V in a wide range of supercap voltages would be the best, but I don't know how to do it...