Dumbledore, as Harry's guardian in the fanfiction, would probably use his influence in the wizarding world. He could make sure that Harry is taught by the best teachers at Hogwarts. He'd also be there to offer advice and guidance, especially when Harry faces challenges like dealing with Voldemort or other dark forces. For example, he might teach Harry some advanced defensive magic privately to better protect himself.
In the fanfiction, Snape could protect Harry from Dumbledore by using his skills in potions. For example, he might create a potion that hides Harry's magical signature from Dumbledore's detection. Or he could use his knowledge of the Dark Arts to counter any spells or charms that Dumbledore might use to keep tabs on Harry. Snape is very intelligent and resourceful, so he could find various ways to physically and magically shield Harry from Dumbledore.
They probably have a very close relationship. Dumbledore would be like a father figure to Harry, guiding him through the wizarding world.
Harry might initially be confused. He has always looked up to Dumbledore, so when he realizes Dumbledore is trying to control him, he could start to question everything he thought he knew about their relationship. He may become more rebellious as a result, trying to break free from Dumbledore's influence and make his own decisions.
It might make Harry more confident. With Dumbledore's training, Harry gains more knowledge and skills, which gives him the confidence to face challenges.
The relationship would become very strained. Harry's rejection would likely make Dumbledore re - evaluate his actions and how he has interacted with Harry. Dumbledore might be shocked at first, since he probably thought Harry was on the same page as him most of the time.
As the story progresses, Dumbledore might try to make amends. He could start revealing some of his secrets to Harry in an attempt to regain his trust. Harry, on the other hand, would be hesitant at first but gradually start to listen and understand Dumbledore's reasons.
One reason could be that Dumbledore had too many other responsibilities in the wizarding world. He was the headmaster of Hogwarts and was constantly involved in dealing with the threat of Voldemort on a larger scale. He might not have been able to give Harry the individual attention and care that a true guardian should provide.
One possible reason could be that Dumbledore wants Harry to have a more normal upbringing away from the spotlight of Hogwarts and his own influence. So he deliberately steps back from the role of guardian.
He becomes more nurturing. Dumbledore, who was mainly seen as a wise leader, now has to be a caregiver. He might show more patience and tenderness as he takes on the role of a father to Harry.
He might give Harry detention. Harry could be made to clean the trophies in the trophy room or help Hagrid with some difficult tasks in the Forbidden Forest under strict supervision.