Maybe Harry is crying because he misses his parents. He often feels the pain of their absence deeply, and in this fanfic, when Sirius sees him, that could be the cause.
One possible reason could be that Harry is feeling extremely overwhelmed with the challenges he faces in the wizarding world. Sirius is like a father figure to him, so in front of Sirius, he can let out all the pent - up emotions. Maybe he's had a tough encounter with Voldemort or his Death Eaters, and the fear and stress finally break him when he's with Sirius.
Well, it could be that he's feeling the weight of his destiny. Harry has so much on his shoulders, like fighting Voldemort. Maybe he just had a particularly tough encounter with the Dark Arts or lost someone dear in the fight against the dark side. Another reason might be his feeling of isolation. Despite having friends, there are times when he feels alone in his battle.
One possible reason could be that Naruto is feeling lonely. Despite having friends, he still has moments when the weight of his past, like being an orphan and ostracized in the village as a child, hits him hard. Jiraiya might see Naruto crying because of these memories resurfacing.
Sirius might immediately rush to Harry and give him a big hug. He's like a father figure to Harry, so physical comfort would be his first instinct.
One reason could be that he's facing extreme pressure in potions class. Maybe he's constantly compared to others, like Snape always having high expectations of him. Another reason might be that he has some kind of emotional turmoil related to his past traumas while in the potions environment. For example, the smell of a certain potion might remind him of a difficult time at the Dursleys.
Perhaps he's feeling isolated. Even though he has friends, he often has to face his battles alone in some ways. Ginny finding him crying could be a moment of vulnerability that she witnesses, and it might be related to his feeling of being alone in the fight against the dark forces.
It could be due to the danger they are constantly in. In the wizarding world full of dark forces, Ginny might be really scared for Harry's safety. She loves him deeply and the thought of losing him makes her break down in his arms.
One possible fanfic could be titled 'The Grief of Harry: When Sirius Fell'. In this fanfic, it might show Harry's immediate reaction of shock and disbelief. He might stand frozen as he witnesses Sirius's death, then slowly sink to his knees, tears streaming down his face as he screams in anguish. His world would shatter, and he'd feel a loneliness like never before.
In the fanfic, Harry might cry because he's now faced with the reality of having to rebuild his life. Before the war, his focus was mainly on fighting Voldemort. But after the victory, he has to figure out things like his career, his relationships, and his place in the new wizarding world. The pressure of all this new stuff can make him cry.
He could be crying out of frustration. In the fanfiction, he might be facing difficulties in his studies or in learning new spells that are crucial for his fight against the dark forces. In the Great Hall, where he is constantly surrounded by students who seem to be doing better or at least not struggling as much as he is, he might feel inadequate and start crying. Also, if there are new threats emerging in the wizarding world and he feels like he's not making enough progress in preparing for them, this could lead to a breakdown in the Great Hall.