>>58160953 (OP)
It seems to me the Genderless/Gender Unknown classification is for Pokémon who overall just don't neatly fit in to exactly either male or female.
>>58161056
>also semi-releated, the "no eggs discovered" group's name would imply that these pokemon are capable of breeding in lore, but there is no method for them breeding known in captivity
Like with the Genderless/Gender Unknown classification, it seems to me that the No Eggs/Undiscovered Egg Group is just a general catch-all classification for Pokémon of various different reasons why they can't breed in the Breeding System of the games. Such as they can't breed at all, just refuse to do so or can only do so in extremely specific means not really possible via the regular method we see get with the games.