It's possible that his ancestors were related to some of the more mysterious families in the wizarding world, like the Lovegoods. Maybe they shared certain magical abilities or eccentricities. They could also be linked to the Blacks, which would mean he has a connection to that complex family tree full of dark and light wizards.
He could discover that he has a long line of powerful wizards. Maybe some of his ancestors were great duelists or inventors in the wizarding world. For example, they might have created spells that are now lost or forgotten.
He might learn about hidden magical talents in his family. For example, perhaps there were ancestors who could communicate with magical creatures in a unique way that was lost over time.
At first, his friends would be shocked. Hermione might think it's some kind of dark magic at first glance. But as Harry shows them what he can do, she would start to analyze it scientifically. Ron would be more awed. He'd be like a kid seeing a new cool trick. They would both support Harry in exploring this new ability, but also be a bit cautious as they don't fully understand where it comes from or what the implications are in their wizarding world.
In this type of fanfiction, the relationship between Harry and Snape can be re - imagined. Snape was Harry's teacher for Occlumency in the books, but often their interactions were tense. Fanfic writers may change this dynamic. They could have Snape be more patient or Harry be more receptive, which would lead to a different kind of mentorship and a new understanding between them.
One interesting lesson could be table manners in the wizarding world. There might be specific ways to hold a wand while dining or proper incantations to say before and after a meal. Another could be how to address different levels of wizards and witches, like the proper title for a powerful elder wizard. And perhaps the correct way to enter and exit a magical room or building, which could involve specific spells or gestures.
Another theme is the discovery of long - lost family secrets. In many fanfictions, Harry or other characters find out about hidden parts of their family history that have been buried for centuries. This could include things like a secret alliance with a dark wizard in the past that the family has been trying to keep quiet.
It could be Dumbledore. He always has a knack for providing Harry with useful tools. Maybe he found this device during one of his travels and thought it would be beneficial for Harry's growth as a wizard.