Harry might react with defiance. He has always been a brave character, so he could look Snape straight in the eye and not show any fear, even though he is in a vulnerable position.
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 trying to intimidate Harry. He has always had a rather tense relationship with Harry in the original story, and this could be an extreme form of showing his authority. Maybe he suspects Harry of something, like being involved in some mischief or having knowledge about a certain Dark Arts item or activity.
Another reaction could be fear. Despite his bravado at times, Snape can be an intimidating figure. If Harry is caught off - guard, he might feel a moment of real fear. His heart could start racing and he might struggle against Snape's hold, but be too afraid to say anything at first.
Another way Snape could comfort Harry is by standing up for him in certain situations. Maybe when other teachers or students are being unfair to Harry, Snape steps in and defends him. This act of protection can be a great source of comfort for Harry, as it shows that someone is on his side even if they have had a rocky relationship in the past.
In some fanfictions, Snape might use his advanced knowledge of potions to brew a special healing elixir for Harry. He could also use his magic skills, like a complex spell specifically designed to mend Harry's wounds, whether they are physical or emotional.
Sure, the Harry Potter fandom is huge and full of creativity. Writers might come up with a story where Harry is Snape's master for various reasons. It could be due to a prophecy or a magical bond that no one expected. In this kind of fanfiction, we might see Snape having to follow Harry's orders, which would be a complete reversal of their normal relationship in the original series. This could lead to some very intense and dramatic storylines.
One possibility could be that in this fanfiction, Snape takes Harry for some sort of training or protection. Maybe Snape realizes that Harry is in greater danger than Dumbledore anticipates and decides to take matters into his own hands. He might take Harry to a secret location to teach him advanced magic or to keep him away from the prying eyes of Voldemort's followers.
In fanfiction, Snape teaching Harry Occlumency is often a very intense and complex relationship. Snape's own mixed feelings towards Harry add layers of drama. His strict teaching methods sometimes seem cruel but are also necessary to force Harry to master Occlumency. Harry, on the other hand, is often resistant at first, not fully understanding the importance and also being put off by Snape's attitude.
Snape is always complex. In this situation, he would be conflicted. On one hand, he has his long - standing dislike for Harry (or rather, his connection to James). On the other hand, as a teacher, he has a duty to take care of a student in distress. Drunk Harry would be a bit clumsy and giggly perhaps. His judgment would be clouded, and he might see Snape in a different light, not as the enemy but as someone who could help him, which could start to shift their relationship dynamic in the fanfiction.