My guess is the voltage - nice!nano has 3.3V on the VCC pin, while the pro micro has 5V (there might be 3.3V variants, but the shops I checked have 5V variants). The SK6812 LEDs are specced for 5V.
That said, mine worked well so far running on 3.3V, but when the battery was low some colors would not turn on.
Bear in mind that my board is handwired (and has fewer LEDs) and I only quickly checked the Sofle build guide (it might have a separate voltage regulator for the LEDs).
Anyway check voltages and if you indeed have 3.3V you might be able to work around it by swapping the LEDs out and hope the replacements are more tolerable to the lower voltage.
Happy hacking!