For some reason, it can do it for 1 side, but not the other. When it fades down it's either skipping some or something, going back up it seems smooth…
FastLED only does RGB, not RGBW.
Yeah, this really needs a separate page.
The microcontroller in each LED takes 2mA on idle. Ouch.
But NiMH cells have a lower internal resistance, and if that resistance is a major part of the resistance to limit the current into the LEDs (as it often is in cheap designs with coin cells, but less often in AA-based designs) you'll probably fry the LEDs quite quickly.
Nice tutorial on power saving stuff on Adafruit. https://learn.adafruit.com/sipping-power-with-neopixels/