Perhaps it was an order from Dumbledore. Dumbledore often had complex plans, and he might have asked Snape to put Harry to sleep as part of a larger strategy against Voldemort. Snape, being loyal to Dumbledore in his own way, would carry out such an order even if he didn't fully understand it at the time.
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.
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.
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.
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 suspects Harry of something. Maybe he thinks Harry is involved in some sort of mischief or is in possession of something he shouldn't have. Snape has always been a bit of a mystery and is often distrustful of Harry, so this action might be his way of getting to the bottom of things.
One possible reason could be Snape's long - standing grudge against James Potter, Harry's father. Since Snape had a difficult past with James, he might project that onto Harry. Another reason could be that Snape is trying to protect Harry in a very strange way. He may think that by rejecting Harry, he is keeping him at a distance from the dangerous wizarding world politics and plots that Snape is often involved in.
Well, it might develop with Harry having strange dreams. Since he has a connection to Voldemort, his sleep state could be a gateway to some sort of shared mental space or prophetic dreams. And Snape would then be left to interpret these dreams when Harry wakes up.