Bellatrix Lestrange could also be a character who interacts with Snape. If Snape goes back far enough, he might try to influence Bellatrix's path and keep her from becoming such a devoted Death Eater. This could have a major impact on Voldemort's power and the overall balance of the wizarding world.
One interesting plotline could be Snape going back and trying to prevent the death of Lily Potter. He might use his knowledge of the future to change certain events that led to her demise.
One possibility could be that he has gone into hiding to protect a secret. Maybe he discovered some dark magic plot and has to keep himself away from the wrong people until he can figure out how to stop it.
One interesting plot could be Severus going back to his school days and trying to prevent certain tragedies. For example, he might try to stop the rift between him and Lily. He could use his knowledge of the future to avoid making the mistakes that led to their falling out. Another plot could involve him changing the course of events related to Voldemort's rise. Maybe he tries to expose Voldemort's plans earlier or influence key characters to oppose him more effectively. He could also go back to a time before he got involved with the Death Eaters and choose a different path entirely, which would then have a huge impact on the wizarding world as we know it.
One interesting plot could be Snape going back and trying to prevent the death of Lily. He might use his knowledge of the future to change certain events that led to her demise. Maybe he would try to expose Pettigrew earlier or find a way to make James Potter more cautious.
If Snape goes missing, Hogwarts would be in chaos. His students would be worried and confused. The other teachers would have to take over his classes, but no one could replace his unique teaching style.
Obviously, Severus Snape is the central character. He is the one who travels back in time, so all the actions and changes are centered around him. But other important characters often include Lily Evans. Since Snape had a deep connection with her, he might try to interact with her in different ways to change the past.
Going back in time gives Severus the opportunity to develop a different relationship with power. In the original timeline, his pursuit of power through the Dark Arts and association with Voldemort led to many problems. But if he goes back, he could use his knowledge to gain power in a more positive way. He could become a powerful force for good in the wizarding world, using his intelligence and skills to promote peace and cooperation. His character would then be seen as a reformed and wiser version of himself, rather than the conflicted and often tragic figure he was in the original story.
It's popular because it gives Snape a chance to rewrite his story. He was such a complex and tragic character in the original series, and in these fanfictions, he can correct his mistakes or make different choices.
One possible plot twist could be that when Harry goes back, he discovers that Snape's situation is far more complex than he initially thought. Maybe Snape was involved in some secret mission that put him in danger, and Harry's interference actually endangers the entire wizarding world in unexpected ways. For example, Snape might be on the verge of uncovering a new dark magic plot that Harry's presence disrupts.