That’s how I interpreted it. For the uConsole – if I remember correctly – they had recommended protected batteries for lack of that circuitery. For the PicoCalc, I believe they integrated the protection circuit onto the product so it isn’t required that the batteries have it. As for the form factor (flat or button top), both will fit, just be extra careful with the polarity with a flat top battery.
If you go to a vape or flashlight shop, they will have some. There are usually a few models, with varying capacity and max discharge rate. For our application, we don’t care about the max discharge rate. Capacity will be around 3000mAH to 3500mAH, but not much above that. Be wary of anyone promising 4000 or more: these batteries don’t exist.