One possibility is that Harry would be extremely hurt and angry. He might immediately confront Ginny about it. He could cut off all ties with her and distance himself from their mutual friends as well, feeling betrayed not only by Ginny but also by the false image he had of their relationship.
It could cause a scandal in the wizarding community. People might take sides, with some supporting Harry and others thinking there must be more to the story. The Weasley family's reputation could also be affected. Ginny's actions might be gossiped about in places like Hogwarts and Diagon Alley.
Well, it could be that Harry has started acting really distant from Ginny. He might be canceling their dates frequently or not being as affectionate as he used to be. In the fanfiction, Ginny might also find some strange gifts or notes that she suspects are from another girl to Harry, which makes her think he's cheating.
One possible reason could be miscommunication. Maybe Ginny feels neglected by Harry because he's so caught up in his own heroic deeds and doesn't pay enough attention to her. So she might seek comfort or excitement elsewhere.
In fanfiction, anything can happen. However, if Ginny cheats on Harry, it would likely shatter the trust in their relationship. It could lead to a downward spiral in the story, with Harry feeling betrayed and perhaps seeking revenge or just distancing himself. This could also change the dynamic among their friends and family, as everyone would be caught in the middle of this drama.
I really hope there isn't such a fanfiction. Ginny and Harry have a strong and loving relationship in the original story, and creating a fanfiction with such a negative and unfaithful plot goes against the essence of their relationship.
He could also be secretly amused. Despite his stern exterior, Snape might see a bit of his own unrequited love in their relationship. So, he might give them a stern warning but not be as severe as he usually is.
Maybe Snape catches them in the middle of a magical experiment gone wrong. Harry and Ginny were trying to recreate an old spell they found in a dusty book, and the resulting chaos draws Snape's attention. He then has to decide whether to punish them or help them fix the mess.
One good 'Hermione Catches Harry and Ginny' fanfiction could be 'The Unexpected Encounter'. In it, Hermione stumbles upon Harry and Ginny sharing a private moment in the Hogwarts gardens. It beautifully captures the shock and confusion on Hermione's face. Another might be 'Caught in the Act', which delves deeper into Hermione's feelings of betrayal and how it affects their friendship triangle.