"Isn't that why you came here? To be with me again?"
But it's pretty weird for Afton to be working as a technician in his own company, isn't it? And anyway, in the beginning of the game, Hand Unit tells you to-
"Please enter your name as seen above the keypad."
...and the name pasted above the keypad is "Mike". So we play as Mike... Schmidt? The guard from the first game? Why? And what about that other stuff that suggests we're Afton? Is Mike Schmidt William Afton?
This left the theory community very confused, so Scott stepped in to clarify with a lore dump in the Custom Night update.
"Father, it's me, Michael. I did it. I found it. It was right where you said it would be. They are all there. They didn't recognize me at first, but then, they thought I was you."
This clicked everything together- Mike Schmidt is the older brother from the FNaF4 family, which is the Afton family. The Logbook would further clarify that Mike is also the FNaF4 dreamer, evidenced originally by the random Phone Guy audio in FNaF4's ambience. It is easy to take all this for granted now, but it was not obvious at the time; It wasn't even well agreed that the FNaF4 family was the Aftons, let alone that Mike Schmidt is Purple Guy's son and the protagonist of several games.
So, here's an important question: Why did Baby mistake Mike for William? In-universe it's presumably because they look similar (killing the theory that Mike is adopted), but that's not what I mean. Why did Scott put that in the story? Why did he write dialogue which clearly implies the protagonist is William, when they in fact are not? How on earth were we supposed to figure that out?
This, I think, reveals the lore purpose of The Immortal and the Restless. It was a piece in the puzzle of figuring out the protagonist's identity, before Custom Night gave the answer away.
The Immortal and the Restless shows us a purple vampire who insists the vampire baby is not his. The joke is that the baby is obviously his, because it so obviously resembles its father. The parallel is to William Afton having a son who very obviously resembles him... who could even be mistaken for him. That's the missing piece to solving the protagonist's identity, to reconciling Hand Unit calling us Mike with Baby thinking we're William. We needed to know that there was an Afton son who closely resembled his dad.
(Also note Baby's initial "I don't recognize you. You are new." on night 2, which was presumably meant to cast some doubt on her later recognition that we are William.)