Upon reading these past few chapters I think that Harry has invented a spell to download Hermiones brain state just before her death and this is what we are seeing with the whole soul explosion when she dies.
We have never seen this happen so far at all in HPMOR, and I would think if this is a common thing then when Dumbledore is trying to prove to Harry the existence of souls this is the evidence he would use to try and prove it to him. The fact that he did not and this only seems to have happened during this one particular incident suggests to me there is...
It's not unique, and Dumbledore did bring it up, actually:
..."How can you not believe it? " said the Headmaster, looking completely flabbergasted. "Harry, you're a wizard! You've seen ghosts! "
"Ghosts," Harry said, his voice flat. "You mean those things like portraits, stored memories and behaviors with no awareness or life, accidentally impressed into the surrounding material by the burst of magic that accompanies the violent death of a wizard -"
[...]
I asked Hermione and she said that they were just afterimages, burn
Fair point, I missed that bit. There goes my theory then