Fwiw, i think the blue brick you linked B-man is a 3 cell battery, many are. It will work, but will not be as robust as a 4 cell (like the Amped or Dakota type). IMO, for many devices, the higher operating voltage offered using 4 cells in series is a better option.
Also, the listed capacity is often the aggregate of the individual cells capacity, not the battery’s voltage basis. The same item might be listed something along the lines of 20000mah (@ 3.6-4.2volts), or 6600mah @ 10.8-12.8volts. The battery you linked is likely just under 7ah @ 12 volts?
Quality lithium cells are pretty much a commodity, in terms of energy capacity, you get what you pay for.