One creative use is apparition into other dimensions or parallel universes. In some fanfics, characters use apparition to cross into different versions of the wizarding world, where things are very different. For instance, a world where Voldemort won the war and they have to use apparition to find a way to fix that reality.
Harry Potter himself is often a popular character in apparition - related fanfiction. Writers like to explore his experiences with apparition, especially as he gets better at it. Hermione is also popular. Her intelligence could be used to explain the more complex aspects of apparition, like the theory behind it.
Apparition in fanfiction can also have different side - effects. While in the original series, the main concern is splinching, in fanfictions, there could be other consequences like leaving a magical trace that can be tracked by dark wizards. This adds an element of danger and intrigue to the story.
One idea could be a character accidentally apparating to a completely unknown and dangerous magical location. For example, they might end up in a forgotten part of the Forbidden Forest where ancient and dark magic lurks. Another could be a young wizard struggling to master apparition and constantly ending up in embarrassing or comical places, like inside a classroom cupboard during a lesson.
Harry could also get involved in the internal affairs of Remnant. Maybe he'd be drawn into the conflict between the different kingdoms or the fight against Salem. His presence could tip the balance in different ways. He might use his magical knowledge to help develop new weapons or defenses in Remnant, or he could use his ability to communicate with magical creatures to befriend some of the unique fauna in Remnant.
Apparition is more likely to be a work of imagination. Usually, such stories are crafted for entertainment rather than being rooted in real events. There might be elements inspired by real-life situations, but it's not a direct account of a true story.