Hola,
I figured at somepoint someone would have a similar problem. I´m no Electric Engineer but I know the battery is a lithium polymer battery. From playing with drones and electric skateboards I know that the standard "nominal" voltage of Lipo batteries in the 3.7V and they should only be charged up to 4.2 V and to extend battery life (at least with my electric skateboards) should not be discharged past around 3.5V. I assume the PCB will take care of the battery charge and discharge. I havent torn into the battery to look at the PCB yet. I´ll post some photos when I get there.
I was curious where you found the small lipo - 10mm x 20mm x 2.5mm cells???? I have been unsuccessful finding replacements based on the product code as well. I did fond some small lipos for older fitbit models. Ususally with lipos this small the batteries are sold with a PCB built in (again from my experience with smaller drones, and I was hoping to find something like that.
