The 300 leds have a quiescent current as I learned here: How do you use an 8X32 led matrix board?
That means if all leds are off, then you still have a current of about 300 mA !
When the powerbank has a USB output of 500 mA, then then is only 200 mA left to light up some leds.
The power management function is confusing. If you run the ledstrip at 5V, then use 5 for the first parameter, and the second parameter is the maximum current that the library allows.
void setup()
{
FastLED.addLeds<NEOPIXEL, DATA_PIN>(leds, NUM_LEDS);
FastLED.setMaxPowerInVoltsAndMilliamps( 5, 200); // set maximum current to 200 mA
...
Do you have a capacitor at the end of cable at the ledstrip and a protection resistor in the data signal ?