Can a power bank power a stepper motor with these specs?
The power bank you link to can deliver a claimed \$\small{2.4 \rm A \times 5 \rm V} = 12 \rm W\$ on one USB port if you use only one port.
Using a step-down DC/DC converter to go to \$\small \rm 2V\$, assuming 85% efficiency, would give you a maximum of \$\small{0.85} \times {\normalsize \rm {12W \over 2V}} \approx \rm 5A\$, which is more than enough.
The claimed capacity of the power pack is \$\small\rm72Wh\$; assuming 75% of that is usable, it should be able to deliver \$\small\rm 2.8A \times 2V = 5.6W\$ to the motor for \$\small \rm 0.75 \times \normalsize{72Wh \over 5.6W} \small \approx 9.5 \space hours\$, assuming a 100% efficient motor driver.
The calculations for the other motor mentioned are left as an excercise to the reader (I have always wanted to say that).