Tatsumi is very likely to be involved as he has a significant relationship with Esdeath in the original story. Her subordinates in the Jaegers might also be part of the fanfic. They could be shown as being protective or having mixed feelings about her pregnancy.
If Naruto is Esdeath's brother in fanfiction, they could embark on adventures across different dimensions. Since Naruto has experience with his own world and Esdeath with hers, they could explore new lands together. They might encounter strange creatures and powerful enemies. Along the way, they could learn from each other's fighting styles and abilities, Naruto teaching Esdeath about chakra and she teaching him about her own brand of combat techniques. And they could also be on a quest to reunite their fragmented family or uncover a long - hidden family secret that has the power to change their worlds.
Esdeath's demise in the manga is quite intense. It's a culmination of her actions and the circumstances she finds herself in. To get the full impact, you really need to delve into the manga pages.
Well, one possibility could be that Naruto inherits some of Esdeath's cold and calculating nature. Maybe he uses her strategic mind to outwit his enemies in the Naruto universe. He could also have some unique abilities related to ice, like Esdeath does.
Another theme is the exploration of good and evil. Esdeath is often seen as a morally ambiguous character from 'Akame ga Kill', and in the Harry Potter universe, she is placed in a new context of good and evil. So, fanfictions usually deal with how she either adapts to the more clearly defined good - vs - evil concept in Harry Potter or challenges it.
The Akatsuki could still be major antagonists. Their goals of collecting the tailed beasts would put them in direct conflict with Naruto, especially if he has the added power from his relation to Esdeath. They might see him as an even greater threat.
In some fanfictions, the plot could revolve around Naruto introducing new forms of combat training to Esdeath's peerage, inspired by his training with Jiraiya. This could lead to the peerage becoming stronger and more versatile. Also, there could be a plot where the peerage has to protect Naruto from those in their world who see him as a threat, due to his unknown powers and origin.
Some common themes could be the exploration of Esdeath's character in a new light as a mother - to - be. It might also include how her pregnancy affects her relationships, like with Tatsumi. Another theme could be the challenges she faces during pregnancy in the context of the Akame ga Kill universe.