I'm, When the charged battery without load with a brightness of about 10-20% by BP nout consumes not more than 0.5A
When the charge consumption is increased to 1.5A, which is consistent with 2A PSU family.
When powered by lithium (3.6 V) of intake banks will be orders of magnitude (12V 1.5A * / 3.6V / 75% (efficiency)) 6-7 Ampere !!!
From 5V it will be of the order of 5A! USB connectors are not designed for such talk! 0.3-0.5V voltage drop (1-2 W and dissipated power) only on it.
And now look at your photos on a USB wires thickness .. At this current drop in on them will not be less than 1V.
Generally, work with an external voltage source begins with 10B. Therefore, if you want to have a backup source, you need to fully assemble it yourself:
Take at least 4 banks vparallel and immediately fed from them to upconverter capacity of at least 30 watts. Raise voltage to 10.5-11V
Or take 3 banks consistently better at 3.85 V, and they immediately lead to a thick wire noutu.