The objective of this prompt is to take the above tropes, and write a story that makes them good.
Step one, set it in the middle ages. The modern setting isn't too impactful on the plot of HP anyway, so it won't be hard.
The world, including the wizarding one, is ruled by a feudal system with a house of lords. The wizengamot, also known as the house of merlin, is a progressive union comprised of the most influential houses of wizarding britain, along with their vassals. It represents the first step towards unified government in wizarding history, and is tasked with the creation and enforcement of law.
It has been 200 years since Merlin's death, and 200 years since his dream of a unified muggle/magical world died with him. Voldemort rises, not on a tide of pureblood supremacy, but on a swell of twisted idealism. He is a manipulative monster solely interested in power, but the platform he he builds is made on the premise that the muggle world must be subjugated for it's own good, that they will tear themselves apart without the guidance of wizards. It still treats muggles as lesser, but instead of like tainted animals it considers them like foolish, dissapointing children. .
Voldemort's rise to power was the first major test of the unity of magical britain since Merlin's death, and was a bloody affair. Many houses were ended, and many more brought low. The house of Potter was one such house, long a vassal they rose by the greatness of others and had gained independance as little as 50 years before Voldemort's rise, in the wake of the war Harry is the only survivor if his house, hidden away after Voldemort's death he returns to the magical world as no one. He is not the saviour, nor a villain, merely another victim. Voldemort was not known to be vanquished by the potters, even though that is what happened, but dissapeared without a trace. His followers collapsed, though some await his return, and the wizarding world is suspended as if in the intermission between acts of a play.
Sickly and frail, Harry Potter is overlooked and underestimated, but while his body is weak his mind is sharp as a blade. He is a good person, but not naiive, and he views the world as defined by the desires of others, and morality as a luxury to be excercised as often as possible, but only when practical. His family rose to prominence by connection to others, and those ties bind him still. Harry knows nothing of politics, and is considered to be nothing by many, but he will rise. He will use whatever scraps of influence or pity he can, any claim, any relation, any agreement, any shred of alliance he can to rise from ignominy.
Harry is raised a peasant and treated as one would an orphan bastard. Vernon is a carpenter, and hates Harry not because of his unnaturalness, (the supernatural was far more accepted back then) but because he small and frail and cannot contribute to the household. Petunia loved her sister, but was embittered to the world that took her from her, and is held backfrom being close to her sisters son by the regrets of her past and by the lingering hatred of the world he represents. Dudley was not unkind to him, but he was always needed elsehwere as the only other able bodied person in a four person household. So Harry grew in solitude, in resentment, and in impotent desperation. He will do anything to be something more than what he is, and when the wizarding world comes along with the opportunity to rise above his limits and pay back the debt he owes to his family he graps it with both fragile hands.
Harry Potter was not taught their ways, nor their games, but he will learn and he will rise. If there is war then all the better, for there is no better time to rise above one's station than when the whole world is on the brink of bloodshed. Voldemort returns and is quietly focused on revenge, but does his best not to let it be known how he was defeated.