Alright so here's some more things for Dante's passive Soul Manip.
Griffon, Shadow, and Nightmare all have "cores" in the original DMC. While Griffon's core is the hardest to see, it is still there, appearing when you ground him and stun him. Shadow's core appears when you deal enough damage to him, as he will break apart into a black puddle beneath the bright red core. (Shadow's core also appears whenever he is about to use an instant-kill attack, acting something like a goad to lure you)
Griffon is unable to regenerate from only his core, or at least his Regenerationn is much slower than his DMC5 counterpart, but he takes extra damage when you attack it. Nightmare ca regenerate from only his core, as we defeat him once before his final encounter and despite "dying" he is completely fine the next time around.
Shadow is the big one here, he explicitly shows that he can and does regenerate from only his core, as when he takes a large amount of damage, he collapses into a puddle, then regenerates back into his panther form around the core.
Ironically, the only major demons without cores are Nelo Angelo (who is Vergil so we know why that's not a thing) and Phantom, which is fine as he seems to be the only major demon that was not explicitly created by Mundus. Or at least, he was never hinted at being created by Mundus.
This actually explains quite a lot. In universe, Dante is so far above these demons that they're basically annoying flys to him, aside from maybe Nightmare. So even if they were able to flee, it's unlikely they would have been able to even survive with the wounds they sustained without some form of Regenerationn. If these cores let them regenerate from only their souls (which would be the cores as we've gone over), it makes sense that they could survive for so long, since Dante would need to actually destroy their souls to kill them, which could prove troublesome if they fled before he could.
tl;dr: Low-Godly makes sense for even pre-DMC5 Shadow and Nightmare. And given Dante can directly attack their cores, it is entirely probable that he has passive soul hax on his attacks.
This is further compounded by TAS, where Dante seperates a demon from someone's soul and body with a sword throw of Rebellion. Holy Manip might work here, but the actual appearance of it is far closer to soul manip in my own opinion.
