Hypothesis: Harry lives in a close to post-singularity universe. The source of magic is a boxed AI, created by the Atlanteans and Harry himself.
Currently, the boxed AI can be manipulated by means of spells,
potions and rituals and is acting as a limited outcome pump. Harry, in his quest to end death, will release the AI from the box, thus bringing about a true singularity end state and the foretold end of the universe as we know it.
The method through which Harry will achieve this (releasing the boxed AI while simultaneously being partly responsible for its creation by the Atlanteans in the past) will be a trick using multiple time turners and something like the algorithm Harry invented in chapter 17 for solving an NP complete problem coupled with Timeless Decision Theory.
If you build a device capable of factorising in less than polynomial time, you have a major building block of a supercomputer. If you can do it in negative time (solution before input) you've built an AI. Harry attempted this in chapter 17 but was stopped by a future Harry with the admonishment "DO NOT MESS WITH TIME" which Harry resolves to obey until age 15. That intervention could have been from an even further future Harry.
The theft of Hermione's body could also have been conducted by an even further future Harry which allows him to pass the questioning of the headmaster.
If Harry can figure out how to bypass the limitations of the time turner, that is all he needs to do to bring about the scenario I outlined, and build an outcome pump that will restore Hermione, be established as the source of magic in the past and the bringer of the singularity in the future.
I assign 60% confidence to this hypothesis.