Perhaps Harry has been snooping around in Snape's private business. Snape is a very private person, and if he suspects Harry of prying into his secrets, like his past associations or his personal research, he would be furious enough to send a Howler.
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 related to Harry's relationship with Snape's house, Slytherin. If Harry has somehow slighted the Slytherin house or one of its important members, Snape, as the head of Slytherin, might send a Howler to put Harry in his place.
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.
Harry might be initially shocked and embarrassed. A Howler is a very public form of scolding, and in front of all his friends and classmates, it would be a humiliating experience for him.
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 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.
Hermione could be the sender. If Snape has made some unfair judgment in class against Gryffindor students, Hermione, with her strong sense of justice, might send a howler to him to voice her protest.
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.
One possible reason could be that Snape is starting to see Harry in a different light. Maybe he realizes that Harry has been through a lot and has a moment of empathy. It could also be a sign of a deeper, unspoken connection developing between them in the alternate universe of the fanfiction.
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.
One possible reason could be that Snape is still holding a grudge against James Potter, Harry's father. He might take out his long - standing anger on Harry. Another reason could be that Snape is trying to discipline Harry in his own strict way, but it ends up being too harsh and making Harry cry.