One possible reason could be that Snape suspects Harry of something dangerous or against the school rules. Maybe he thinks Harry is involved in some secret Dark Arts activities and ties him up to prevent him from causing further trouble or escaping while he investigates.
One possible reason could be to protect Harry. Snape might believe that by tying Harry to the bed, he can keep him in a safe place away from immediate danger. Maybe there's a threat in Hogwarts or outside, and Snape thinks this extreme measure is necessary to ensure Harry's safety.
Well, perhaps there was an emergency at Hogwarts. Maybe some dark forces were approaching, and Snape, being a powerful wizard and a Hogwarts professor, felt it was his responsibility to pick Harry up. Harry was always a target for the dark side. Also, it could be that Snape had some new information about Harry's family or his destiny that made him decide to take Harry under his wing, so to speak, by picking him up.
One possible reason could be that Harry has made a significant mistake in Potions class. Maybe he has endangered himself or others during an experiment, and Snape, being strict about safety and proper procedure, sends the Howler as a very public scolding.
It could also be for some sort of magical experiment or study. Snape, being a Potions master and a very knowledgeable wizard, might need Harry in a dormant state to study something about his unique magical abilities. For example, his connection to Voldemort might behave differently when he is asleep, and Snape wants to observe this.
It could also be due to some external factors. Maybe there are threats from dark forces that he doesn't want to involve Lily in. If he is getting deeper into the dark arts or some dangerous situations, he might choose to give up on her to protect her from the potential harm that could come her way because of his associations.
One possible reason could be that Snape is secretly trying to protect Harry. Maybe the potion has some sort of protective charm or antidote against a dark magic threat that Snape has foreseen. He may not show it openly, but his actions are driven by his long - standing, complex feelings towards Harry's mother and his sense of duty.
One possible reason could be that Harry is afraid of Snape's intimidating presence. Snape has always been strict and rather unfriendly towards Harry in the original series, so in the fanfiction, this fear might be amplified, causing Harry to run. Another reason could be that Harry has stumbled upon something he shouldn't have seen that involves Snape, and he's running to avoid getting caught.
One possible reason could be Snape's sense of duty to protect Hogwarts students in general. Even though he dislikes Harry, he might put aside personal feelings to ensure the safety of a student in a dangerous tournament like the Triwizard Tournament. Another reason could be Dumbledore's influence. Dumbledore trusts Snape and may have asked him to keep an eye on Harry during this event.
Maybe Snape suspects Harry of being involved in some sort of dangerous activity related to the Dark Arts. Pressing him to the wall could be a way to force Harry to come clean about his actions or any knowledge he might have. It could also be that Snape is acting out of his own insecurities and pent - up emotions towards Harry, which he has been suppressing for a long time.
Harry might initially be shocked and angry. He would probably struggle against the restraints and demand to know why Snape is doing this. He could yell at Snape, asking for an explanation and protesting his innocence if he believes he has done nothing wrong.