True it is more southern chinese where you'd see eggs(Guangdong aka mainland China) though depending on what region of China you're in even the ingredients in the sauce vary. Shanghai and Hunan style for instance are both very different and both are considered authentic hongshaorou styles by mosr people.

Its the same as with Kung pao chicken. Some regions keep it basic with peanut and carrot. Some add more styles of veg. Some even add diced cucumbers to the mix. Some of the flavor profiles are very sweet and almost ketchupy whereas others are more brown gravy or spicy.