Snape could be initially shocked. He's used to seeing Harry as a rather tough and rebellious student. So, seeing Harry cry might take him aback for a moment. Then he might become a bit more guarded and try to figure out if Harry is faking it or not.
Maybe Harry is under a great deal of stress. He has so many burdens on his young shoulders, like fighting Voldemort, protecting his friends, and dealing with the secrets of his past. Snape has always been a rather intimidating figure to him, but in that moment, the pressure might just be too much, causing him to break down in front of Snape.
One reason could be the stress of fighting Voldemort. Harry has so much on his shoulders, and McGonagall is a figure of authority and comfort. He might break down in front of her when the pressure becomes too much. For example, when he has to face difficult decisions like whether to sacrifice himself or when he feels responsible for the safety of his friends.
In some fanfictions, Snape might awkwardly try to comfort Harry. Given his own complex personality, it wouldn't be an easy or natural gesture for him. He might pat Harry's shoulder stiffly or offer some gruff words of reassurance like 'Pull yourself together, Potter.'
She might immediately comfort him. McGonagall is a strict but kind teacher. She could put a hand on his shoulder and say soothing words like 'There, there, Mr. Potter. It will be all right.'
Sirius might immediately pull Harry into a tight hug. He would be very protective and try to comfort him. He might say some soothing words like 'It's all right, Harry. I'm here for you.'
One common theme is regret. Snape often cries due to the many regrets in his life, like his role in Lily's death. Another theme is loneliness. Fanfictions often depict him crying because he feels so alone in his world, with his secrets and his unrequited love.
There are harry potter cries fanfiction because it allows fans to add their own interpretations of emotional moments. The series has many tragic events, and seeing Harry cry in fanfiction can be a way to further process and expand on those events. It also gives fans a chance to create new storylines based on his emotional reactions.
Snape might be initially taken aback. He could hide his surprise behind his usual stern facade and perhaps try to maintain order, but secretly be a bit worried.
Snape might initially be suspicious. He has always had a distrust of Harry, so he could think it's some sort of trick. But then, as a Potions master and a teacher, he might also feel a sense of responsibility and try to help.