One possibility is that Umbridge, despite her cruel nature, sees some potential in Harry for her own gain. Maybe she tries to mold him into a perfect little wizard according to her strict and often wrong ideas. She could isolate Harry from his friends and force him to follow her rules blindly, which would create a lot of internal conflict for Harry as he tries to resist her brainwashing while living under her roof.
Well, in this fanfic, Umbridge might adopt Harry to use him as a pawn in her political games within the wizarding world. She could parade him around as a sign of her 'benevolence' while secretly trying to suppress any signs of rebellion in him. Harry, on the other hand, would be constantly looking for ways to escape her clutches and get back to his real friends and the fight against Voldemort.
In a 'Harry Potter adopted by Umbridge' fanfic, it could start with some sort of legal loophole or magical obligation that forces Harry into Umbridge's care. Umbridge would likely impose her extreme views on discipline and blood purity on Harry. She might even try to rewrite his history of fighting against Voldemort to make it seem like she was the one guiding him all along. Harry would have to struggle not only with her daily abuse of power but also with the false image she tries to create of him in the wizarding community.
Chapter 27, "Signing Jiang Yan is fine, but you have to follow along too.", is the clearest early answer because it turns Signing Jiang Yan's situation into a concrete plot event. The chapter gives readers a real answer by opening on They had spent an entire year gradually inviting a few people.
Chapter 348, "Zhu Ling in Dire Straits, Eight Camps Martial Contest, Betting Five Years—East Ridge Has Fallen!", is the clearest early answer because it turns Zhao Hu's situation into a concrete plot event. It opens with If you defend or attack the stage successfully, you can earn one... and closes on This only made Zhu Tong angrier..
Chapter 160, "The Mushroom-Picking Party of Six", is the clearest early answer because it turns Jiang Li's situation into a concrete plot event. It opens with As the sky gradually darkened, the originally mild drizzle began to...
Chapter 102, "The production team can't take a joke!", is the clearest early answer because it turns Zhao Lang's situation into a concrete plot event. A useful checkpoint is the way the scene starts with When the camera cut back, the three of them had already returned to...
Chapter 337, "Major Changes in Xia City, the Richest Person in Great Xia", is the clearest early answer because it pushes Ming Yue into a new phase or setting. Early on, As for the Artifact Refining Hall, they can produce dozens of.... By the end, She held a Bone Fan in her left hand, gently fanning Xia Yusheng,.... Inside the broader power growth storyline, the chapter closes with After all, it's not like she was asked to eavesdrop, and even if she did, she didn't have the capability for it.
Chapter 354, "Mr. Luo, Aren't We Unfamiliar?", is the clearest early answer because it turns Zhao Lang's situation into a concrete plot event. The chapter gives readers a real answer by opening on Lin Manru simply couldn't believe what she had heard.
Chapter 61, "Young Master Before vs After Going to the Countryside", is the clearest early answer because it turns Jiang Yan's situation into a concrete plot event. A useful checkpoint is the way the scene starts with Hahahaha, oh my god, Jiang Li's mouth is even more venomous.
Chapter 34, "Official Recording!", is the clearest early answer because it turns Xiang Hao's situation into a concrete plot event. Early on, Seeing that the public sentiment wasn't quite right, Su Yinwan felt.... By the end, Now that Lili is misunderstood, they start to kick us while we're....
Chapter 331, "Zhu Shun and Huang Tianxi, the 3rd Year Cold Yuan Banquet of Great Xia, and Xia Yuzong (Part 4)", is the clearest early answer because it turns Political Hall's situation into a concrete plot event. A useful checkpoint is the way the scene starts with Follow me closely, don't get lost; why are there so many people?" Zhu... and follows through with After sitting in the main seat, he suddenly raised his head and....
Chapter 15, "The Autistic Teen Jiang Shixu", is the clearest early answer because it turns Jiang Shixu Jiang's situation into a concrete plot event. It opens with Jiang Shixu woke up from those nightmares filled with blood and...