OK, so just to start this out, I wanna put out there, I very much enjoyed this oneshot, and I do hope we get to see some more short stories featuring the same main characters...that said...
I don't think it'll actually get serialized. sure, it was a good read, but one major issue with serialization would be creating a continuous storyline, it seems like this would make for a great series of mostly unrelated horror short stories featuring the same main characters...but if you try and give it some overall story then you'd either have to
1: have some entity with near absolute control over those soul stones and more or less control of the undeads AND a reason why it can't just off the MC as he tries to put an end to it all. I mean, I suppose it could go like Fairy Tail where the main big bad actually wanted to die and made him for that express purpose, but the MC can't instantly start strong enough to end it or there'd be no story...so then the MC would need to get regular powerups which would be hard to mesh with his character...I mean he's not some fantasy mage or fighter who can just learn new more powerful moves or earn a better sword, so what would he get? faster transformations, more advanced autopsy techniques, and sharper knives?
OR
2: you'd at least need to give him some goal to work for, like restoring himself to proper life instead of undead life, but that just doesn't seem to fit either since he's clearly comfortable with his current freely shape-shifting form. and no, just having "stop the other mindless undead from ravaging humanity" would not work as a goal for him to work towards, cause without a cause he CAN stop, there'd never be an end or any notable feeling of progress and if there IS some force/entity he can stop then it falls into case #1
if you just throw him out there fighting an endless series of undead with no progression events, eventually it's just gonna be a repetitive mess that everyone abandons out of boredom BUT if you make it a special once in a while set of well written short stories, then it works without being so constantly repetitive as to turn readers off
...of course, I cannot predict every eventuality, so there's always the chance the author has something planned that would work out, but I'd say a successful serialization of this is the least likely of the probable outcomes