One reason could be that she's trying to break his will. Just like how people can be broken down by being treated as less than they are. Another reason might be that she has some strange, twisted idea of 'caring' in her deranged mind. She could think that by treating him like a baby, she can control him better, like how you can control a small child more easily than an independent person.
Maybe she wants to humiliate him. By treating him like a baby, she can make him seem weak and powerless.
Well, it could add a really strange and unexpected dynamic to the plot. It might make the story more about Bellatrix's warped sense of power and control. Maybe she's using this 'baby - like' treatment to manipulate Harry in some way, like trying to break his spirit more easily by infantilizing him.
Perhaps Draco has developed some sort of complex feelings towards Harry. He could be secretly attracted to Harry and treating him like a baby is a way to get closer to him without admitting his true feelings. Or it could be that Draco has changed as a person and now views Harry as someone who needs his support and guidance, just like one would for a baby.
If such a fanfiction exists, it would likely be a very radical re - imagining of the characters. Bellatrix is a villain in the original, and this would completely change her role in a very unexpected way. It might also change the way readers view Harry's early life and the nature of the relationship between the two characters.
One possible reason could be that Voldemort sees Harry as a symbol of innocence that he wants to corrupt. Just like how he enjoys toying with his enemies, treating Harry like a baby might be a way to belittle him and make him more vulnerable in his eyes.
I'm not sure if there is such a specific fanfiction. It's a rather unusual and probably not very common concept within the fanfiction world. The general fanfiction often focuses on more mainstream relationships and storylines in the Harry Potter universe.
It would be very strange and likely a very dark fanfiction. Bellatrix is a Death Eater and Hermione is a good - hearted Gryffindor. The idea of Bellatrix being involved in delivering Hermione's baby goes against their normal character dynamics. It might involve a very convoluted plot where some sort of dark magic or forced situation has led to this scenario.
Maybe it was a last - minute decision by James and Lily. They might have thought that having Bellatrix as a godmother would offer some kind of protection. After all, she was a powerful witch. Or perhaps there was some sort of old family pact or agreement that made her the godmother.
One reason could be revenge. Bellatrix might want to get back at Harry for causing problems for Voldemort and the Death Eaters. Kissing him could be a form of humiliation. Another reason could be a power play. By kissing Harry, she shows that she can get close to him and has some sort of control over the situation.
Often, in such fanfictions, Sirius may not trust Harry with certain information about his parents or the wizarding world because he believes Harry is too young to handle it. So, he keeps things from Harry, which can lead to conflicts between them. Harry may feel frustrated that Sirius doesn't see him as a capable young wizard, while Sirius is just trying to protect what he sees as Harry's innocence.
It would be a very strange and complex fanfiction. Bellatrix is a Death Eater and much older than Harry. But in such a fic, perhaps it could start with some sort of dark magic influencing Harry's mind, making him see Bellatrix in a different light. Maybe he would be on a mission to understand the Death Eaters better and in the process, he gets too close to Bellatrix and they end up having a relationship that defies all logic and the norms of the wizarding world.