Math is your friend. Mah is capacity. Mutilply capacity by volts to get milliwatt-hours. I'm too lazy to do it but basically it will be the same for 5V, 12V and 20V.
I do agree it is a bit odd they list capacity as 11k mah when it can't even deliver it at 5V. I would guess 11k mah is the nominal capacity of the 3.7V cells.
This. Before the Chinese junk electronics invaded Amazon, eBay, etc, a power supply was rated for its capacity @ output voltage. Then the generics, even if trying to be honest (although still misleading) stated spec'ing what the capacity would have been if the cells were in parallel inside, never mind that they're not in parallel, not the output at the intended use as a power supply.
It can't deliver that at 5V because of buck switching losses to drop the series cells' voltage down to 5V.
Capacitor inside, unlikely more than a minimal value in the voltage buck/boost circuits. Otherwise that would be drained almost instantaneously in a jump start scenario, offering nothing useful. It's just an overrated example that "might" jump start a small engine if nothing else is wrong with it besides the battery being drained, not too far.
In that case the moment you hook it up it is putting some charge into the primary battery so both are working in parallel with the primary supplying more of the current. Cell internal resistance will keep it from bursting into flame for the brief seconds it can provide current before dropping too low in voltage, and there's probably a thermal cutout in the protection circuit. Then again maybe not - Chinese. It might just melt some trace on the circuit board or connector and that's the hoped fail safe.