In Twilight fanfiction about Esme's pregnancy, it often explores the reactions of the Cullen family. They would be overjoyed as Esme is like a mother figure to them. For example, Carlisle would be extra protective, and the younger Cullens might start planning for the new addition to the family in their own unique ways.
One common theme is friendship. Since Esme and Leah are from different 'groups' in the Twilight world, their friendship is often explored. Another theme is acceptance. Leah has to accept Esme's way of life and vice versa.
One common theme is the mother - daughter like relationship. Esme often takes on a maternal role towards Bella. Another theme is protection. Esme wants to protect Bella from the dangers of the vampire world.
One aspect to look forward to in these fanfictions is how Esme and Carlisle's relationship might evolve during this time. Carlisle, being a doctor, would be very involved in the medical aspects of the pregnancy, but their emotional bond would also grow deeper. They might have more tender moments together as they anticipate the arrival of their child.
There could be a new level of intimacy. Sharing this experience of pregnancy would bring them closer together. They would have more private and tender moments, talking about their hopes and fears for the future. Esme might rely on Carlisle more than ever, and Carlisle would feel a greater sense of responsibility towards her.
In these fanfictions, Carlisle could develop by becoming more involved in the family on an emotional level. He's always been a bit reserved, but the pregnancy could break down some of those walls. Esme might grow in confidence as she realizes she's bringing new life into the family. She could also become more assertive in protecting the unborn child, which is a new side to her character. As they go through this journey together, their bond as a couple could strengthen, and they might start to understand each other in ways they hadn't before.
One great 'Twilight' Esme and Carlisle fanfiction is 'Eternal Bond'. It beautifully explores their relationship's early days. Another is 'Unspoken Love' which delves into the unspoken emotions between them. And 'A Love Beyond Time' shows how their love endures through different challenges in the vampire world.
One common theme is their backstories. How they came to be vampires and how they found each other. Another theme is their relationship development, like how they deal with the challenges of being in a relationship in the vampire world.
You can start by looking on popular fanfiction websites such as Archive of Our Own (AO3) or FanFiction.net. Just use the search terms 'Twilight Isle Esme' and see what comes up.
There are fanfictions that expand on the events that could have happened on Isle Esme. Maybe they include new characters or different challenges for Bella and Edward while they are there. It could be about how they deal with the isolation in a more complex way than in the original story.