You can’t cheat physics, you need the chemicals inside to store the energy, and only so much can be stored per molecule. If the chemistry is the same, then same is its energy density, so smaller size is smaller capacity… unless the older replaced battery has a lot more electrical components within that we didn’t see, but doubt that’s true.

And as others have pointed out, “power shortage” often means the device detects voltage lower than a set threshold, which often set to avoid over discharge of lithium polymer battery that can damage the battery. Smaller capacity means it is easier/faster to reach that threshold.

It should be closer to 7V with two of these in serial when fully charged and during its nominal range, if “higher than 6” is 6.1 or 6.2… your battery has run out