I think the egg man is not a character in deltarune or undertale, they are a meta commentary.

the egg man, to me, seems like they are the manifestation of the dream toby had. more importantly they seem like they are a manifestation of motivation and inspiration from other works of fiction and real life.

the man is always in a room in-between, like the motivation and process that comes after being inspired by something and the next thing being made.

the man comes from a world that was painted over, replaced, like how a work that is inspired by something replaces that thing to the creator. even if the old work is still there, it cant be viewed now without thinking of the new.

the eggs are small things that are carried out of fiction into the truth, from dark world to light world, like the impact media has on us.

in chapter 5 when asking about the eggs we missed we are told we see a repeating pattern of trees as we look in the distance, like how all fiction has its inspiration from somewhere and has created an infinite loop of inspiration

the egg man is a story teller.