Just to get this out of the way Obito came to HP dimension because let's say when he was dying in an attempt to delay kaguya's recovery he switched the dimensions but got lost in between, everything in naruto still plays out as it did just obito ended in HP world.
Also Harry will not be OP people like dumbledore and voldemort (with a body) would destroy him. I am bringing threats and powers to level the playing field and increasing the power and skill of people like voldemort and dumbledore to allow them to keep pace. Also Harry will not be pulling susano'o and amaterasu or even Tsukuyomi any time soon if at all, he may be powerful but compared to shinobi yeah no so his use of the Mangekyo is limited and limited to his right eye.
Obito appeared in swirling vortex and fell the ground he felt himself dying. At the very least he managed to delay Kaguya. He looked around he knew he wasn't in his world the odds of him landing in his own after being thrown into the vortex between worlds was so astronomical that only Naruto could be that lucky. He let out a choking laugh, this was an end fitting for someone like him, a criminal just another dead body if there was sentient life in this world he would most likely be just another body, a case that was never solved. Though it wasn't a bad place to die the middle of forest, it reminded him of Konoha, reminded him of home.
He heard the crunching of twigs and turned his head. He saw a little boy that couldn't be any older than seven wander in. He was sniffing and muttering something in a foreign language. Obito saw he was holding his right eye and blood was dripping from it. The boy stumbled and his slipped for a moment allowing Obito to see his right eye or rather where his right eye should have been. He had caused and seen enough injuries to know that the boy's eye was lost.
The boy let out a cry of panic as he laid eyes on what most likely looked like a dead body. Even though he knew it was pointless the odds of his language existing in this world much less this boy understanding it were non existent, he still called out to him. "Boy come here." he gestured hoping the boy would understand, it seems he did as he slowly came towards him flinching as yet another piece of Obito's body turned into dust and vanished in the wind.
The boy bent down and said something in a semi comforting tone before he got up most likely to get help. But Obito grabbed him by the shirt stopping him, he knew there was no chance for his survival. He pulled the boy towards him even as he struggled to get away no doubt thinking Obito had some kind of harmful intentions, but even weakened as he was a small child who was much too skinny stood no chance.
The boy watched in horrified fascination as Obito, still holding him, reached for his own face the boy nearly threw up when he saw Obito pluck out his own eyeball. Than he began to reach for the boy himself with that same hand. His hand reached the boy's own damaged eye socket realized he needed to remove the old damaged eye Obito used his chakra to stick the boy's shirt to himself before using his now free hand to remove the boy's damaged eye. The boy panicked when he felt Obito remove his eye but that his hand glowed green and he was frozen in shock. He placed his eye in the boy's right eye socket. For a moment it was as if he was looking out of the rinnegan as he saw his own decaying body his chakra being destroyed by the all-killing-ash-bone. Then the image cut off and the boy collapsed to the ground holding his eye.
Seven year old Harry Potter was having a really bad day…well more like a really bad life. When he was a baby his parents were killed in a car crash (though his aunt always tried to tell him they were drunks something told him she was wrong) he was left with his relative who despite claiming they took him in out of the kindness of their hearts (which he seriously doubted. He knew someone or something was threatening them, his cupboard allowed him to hear almost everything in the house including them arguing about why they couldn't get rid of him. Then today he cousin had ambushed him and held him down even going as far as to pull a knife so "everyone will know you're a freak" before he slashed Harry's eye. Luckily for him it seemed most of his gang didn't expect him to actually cut Harry so they ran and grabbed an adult causing Dudley and his remaining gang to bolt. Harry ran off trying to go home knowing that nothing would be done about his cousin or Harry would probably be scolded for ruining his knife.
He stumbled into the woods when he came across what seemed to be a dead body before he saw it moved and realized it was alive. When the man lying on the ground called out to him Harry moved closer, then a piece of the guy's body peeled off and was caught by the wind, like he was made out of burnt firewood. Harry bent down and told him he was going for help when the man grabbed him with surprising strength. Harry struggled but the just pulled him closer, he watched with horrified fascination first with the fact that the man's eyes were blood red with strange markings then as he pulled out his own eye. Reaching towards Harry, the man let go of his shirt but for some reason he was still stuck and unable to escape. Harry felt the man's hand reach into his eye socket and pull out his ruined eye. Than the hand holding the man's eye began to glow green before he placed it in Harry head. When he pulled back he was surprised he was able to see out of his eye again yet everything looked strange more clear and slower as if it was all moving through syrup. He looked at the man's body and recoiled it looked like he was being eaten from the inside out.
Than agony enveloped him, his right eye burned as he felt to the ground clutching his newly acquired eye. Unknown to him his magic had first turned the eye into his own making a part of his DNA and unknowing adding chakra to his body but by doing so it reactivated the Potter family curse of eyesight. The reason all Potter men were forced to wear glasses. The blood wards sensing an attack on its charge also reacted. The three types of magic fighting left a strange result. His entire body began to burn as his magic was forced to make chakra coils to allow his body to survive the transplanting of the eye, this would have been impossible if it was not for the minute residue of Juubi chakra, the creator and original source of all chakra. Of course there needed to be a source of chakra for these coils to draw from so they tried for the magical core but that was not chakra. Realizing it's charge was about to die the blood wards abandoned their nearly successful attempt to destroy the curse, and began to force Harry's magical core to adapt.
When all was said and done Harry had a almost completely new layout of magic. It had merged with his new chakra to form some kind of hybrid of the two. He could still perform magic but accident magic would mostly become a thing of the past. In result of his eyes his left eye no longer had the curse but his right eye had a stranger affect to the curse and in a way it was good. The curse was constantly trying to degrade his eye sight down to a poor level but the sharingan was far too powerful to affected meaning that despite the fact that he should have been able to turn the eye on and off it was stuck on as it was constantly fighting against the curse, of course the blood wards were doing their best to fight back by powering the sharingan in an attempt to push the curse back.
When Harry opened his eyes he saw that barely anytime had past before his eyes landed on the man who gave him his new eye. Only for them to widened in horror as he saw that there was now a gaping hole in his chest and he looked like the slightest breeze would scatter him. The man smiled at him seeing he was awake. "Watashi no saigo no kōi wa yoikoto no hitotsu ni naru koto ga dekite ureshī." the man said before he shattered into thousands of flakes and scattering to the winds. Harry closed his eyes and looked down after a few moments he realized it was raining. Opening his eyes he saw that no it wasn't rain, he was… crying? He wiped away his tears in surprise. He couldn't remember the last time he cried, it never solved any of his problems so eventually he just stopped crying.
Harry heard a teacher calling out for him and decided to get this over. The teacher found him with his still bloody eye. The woman began to look his over wiping away the blood when the blood was gone she looked him in the eye and screamed. Harry's eyes widened he had forgotten that he now had the other man's eye and that it was blood red. She couldn't tell anyone he would get into trouble! Harry was panicking his magic surged yet not in it's usual manner with it's new coils it was unable to react as it normally would have. Instead it surged into his new right eye the markings spun and put a single thought into her head, there is nothing you saw in his eyes that you found unusual. Of course unusual was a subjective term the woman saw the amount of blood and deep scar and assumed correctly that his eye had been ruined thus what she thought she saw were the ruined remains of his old eye.
The woman calmed down and looked guilty. "I am sorry Harry I was just surprised." she pulled him into a hug and he stiffed unused to non harmful physical contact. "It will be okay you'll see." she told him, before she stood up and grabbed his hand. "Now let's get you to the nurse's office." she said leading him back to the school.
Harry laid down in his new bed, the Dursley's realizing that people were now suspicious after their son carved out his cousin's eye. Moved him to the smallest bedroom in the house to cover for themselves. Strangely it seemed whatever he did to Miss Helens affected everyone else as well because whenever someone looked at him they only saw the ruined eye not his new and strange eye and that was how he became half blind.
He felt exhausted after a long day. As he drifted off to sleep his mind was filled with images of battles between gods and men. Of two young men, one who glowed as if he was the sun itself and the other who seemed to darken the area around him merely by existing. It was also here he learned the name of his new eye. Sharingan. As he felt himself drift off from this vision he felt happy for some reason when the man of light shook hands with the man of darkness.
Done! So yes Harry saw the end of the fight with Kaguya because Kakashi at the time still had obito's sharingan. Also Yes Harry's accidental magic is now channeled through his right Sharingan. Oh and yes I did use the whole 'potter family is cursed with poor eyesight' thing big deal. oh and Obito's last words were 'I am glad my last act could be one of good.'