Some might be in shock. After all, Harry has been such an important figure in the wizarding world for so long. His friends like Hermione and Ron would probably be very worried about him and try to find out where he went. The Ministry of Magic could be in a panic, fearing that without Harry, they'll be vulnerable to new threats.
Some might be shocked and feel betrayed. Harry is a hero to many, so his departure could leave them feeling abandoned. Others might understand his need for a break and respect his decision.
In a fanfic, Hermione might initially be in denial. She would keep expecting Harry to return any day. She would go to their old haunts in Hogwarts, like the library or the Gryffindor common room, and just sit there, reminiscing. As time passes, she realizes she has to move on. She starts teaching at Hogwarts and imparts her knowledge and the values Harry also held dear to the new generation of students.
Hermione could accompany him. She's always been by his side and would likely follow him out of loyalty and a thirst for new knowledge. Together, they could explore new magical theories in different parts of the world. Another possibility is Hagrid. He has a soft spot for Harry and might want to protect him on his journey. He could introduce Harry to different magical creatures in other countries.
Well, it could cause quite a stir in the wizarding world. First, the relationship between Harry and Draco has always been complex and full of rivalry. If Harry leaves Draco for Ginny, the Malfoy family might feel a sense of victory in a strange way, as Draco has been in this sort of unspoken competition with Harry. For Ginny, it would be a big step forward in her relationship with Harry. And among their friends, like Hermione and Ron, they might have mixed feelings. Hermione might be worried about how this would change the dynamics among them all, while Ron would probably be more focused on how it affects Harry's happiness.
There's also 'Farewell to Magic' in which fem Harry leaves after a big magical war. She realizes that the wizarding world has changed too much and she can no longer find her place there. So she travels far away to a place where magic is just a faint memory and builds a new life from scratch. She has to learn how to adapt to a completely non - magical environment which is full of challenges but also new opportunities.
Some authors write it because they want to explore different character arcs. Harry's character is so iconic in the original series. By making Harry female and having her leave the wizarding world, they can create new and unique storylines that deviate from the traditional narrative.
One interesting scenario could be Harry Potter starting a new life in the Muggle world and using his magical skills in secret to help people. For example, he might use magic to heal the sick in a Muggle hospital without them knowing. Another could be him exploring different magical cultures outside of Britain, like those in Asia or Africa that are not much explored in the original books. He could learn new spells and magical techniques and bring them back to the wizarding world in the future.
In fanfiction, Harry Potter can change the Wizarding World in many ways. For example, he might introduce new spells or magical concepts that were not in the original series. He could also have different relationships with other characters, which in turn would affect the social dynamics of the Wizarding World.
One possible reason could be the trauma he has faced. Harry has endured a great deal of pain, from the loss of his parents to the constant battles and threats in the wizarding world. He might want to escape all that and find peace away from it.