Issue with my solar charger using LM2596
with no load on the output of the LM2596 module, make sure that the output voltage is 5V as you expect, if not tweak the potentiometer until it is, Always turn these things slowly, I have had multiple of these modules detonate if the wiper arm gets too close to ground (too high a voltage on the output capacitor)

With a load connected, if this drops to 1.6V again, does the solar panel voltage on the input also fall? if the power bank is trying to charge at a higher current than the panel is capable of, it may pull down the output voltage,

If the output is being pulled down, you may have to add some resistors to the USB data lines to tell the power bank to use a lower charge rate, not all power banks actually respect this, but it may help,