There are people who better understand retro FX than me. - This video should give you a better clue to what is going on:
But, you have think about it differently. The NES and GB/GBC doesn't "fade" alpha, but shifts the color palettes and lowers brightness of the BG and Sprites. Along with the slower, tick based, processers of the systems is what create that unique NES "Fade".In retro development, everything is done manually. But I use GBStudio which has the fade built in.
In modern development, you will probably have to recreate this manually as well. Shifting each color closer to black from .25 to .5 seconds each "tick". There probably a billions ways to do this. Mostly likely, someone has already made a shader that can mimic it.