Harry could be initially quite nervous. He's used to Severus being his strict professor. But as they explore Diagon, he may become more curious. He might start asking Severus a lot of questions about the different shops and the history of the place. And if Severus shows any kindness or protection, Harry could gradually warm up to him.
In this fanfiction scenario, they may encounter a series of spells gone wrong. Some young wizards might be practicing magic in the alleyways and accidentally send spells their way. Also, they could meet a mysterious wizard who seems to know a lot about Harry's past and Severus's secrets, leading them on a new quest within Diagon.
Well, in some fanfictions, it could be due to a powerful spell gone wrong that transfers the ownership to him. Maybe a spell meant to protect Diagon Alley's property rights backfires and suddenly Harry is the owner.
Harry's reaction could be a mix of fear and defiance. He's faced Voldemort multiple times, so he won't be completely helpless. He may try to understand Severus' psyche, remembering that Severus has always had a somewhat ambiguous relationship with him. He might try to appeal to Severus' better nature if he believes there is one. Harry would also be thinking about how this situation affects the overall fight against the Dark Arts and Voldemort. He might see it as a setback or an opportunity, depending on how he can turn the situation around.
Maybe it's a new character created by the fanfiction author. This new character could have special abilities or a unique backstory that ties into the reason for escorting Harry to Diagon Alley.
Well, Severus could be quite sneaky about it. He might start observing Harry more closely in the corridors and classrooms. If he notices signs of abuse, like Harry being overly withdrawn or having unexplained injuries, he could enlist the help of other trustworthy faculty members. He might also try to give Harry some extra tasks or projects in Potions class to keep him occupied and away from his thoughts about his family situation. This way, Severus can gradually build a relationship with Harry and offer him some form of support without making it too obvious at first.
Severus might initially be shocked. He could then feel a sense of protectiveness over Harry. He might start to secretly look out for Harry, like making sure he has enough to eat at Hogwarts and is safe from further harm.
He might have to deal with a lot of administrative work. Running Diagon Alley means taking care of all the shops, making sure the wizards and witches who work there are happy, and dealing with any disputes. For example, if two shop owners have an argument over a piece of land in Diagon Alley, Harry would have to step in and sort it out.
Harry might be extremely hurt. He could initially feel a sense of shock and disbelief. After all, he may have started to develop some feelings of trust or kinship towards Severus. Then, he might turn to anger. Anger at being rejected, especially if he doesn't understand the reasons behind it. He could also feel a sense of loss, as if he has been deprived of a chance at a real family connection.
Harry might be deeply hurt. He may initially be in denial, not believing that Severus is rejecting him. After all, he may have felt a strong connection. So, he could try to reach out to Severus multiple times, hoping to change his mind.
Severus is a very observant character. He may notice that Harry has a lack of certain basic skills or knowledge that a normal - cared - for child would have. For instance, Harry might not know how to handle simple social situations in a healthy way or might be overly defensive. This could lead Severus to suspect that Harry's home environment, where he should have learned these things, is not a healthy one and that he might be suffering abuse.