The mana core is just in place of their "life force". I dislike using that term but that's what it is. The "immortal being regenerates unless you behead it" thing is in multiple versions of vampire myths(some as extreme as staking them in the heart, beheading them, and burning them). The mana core cannot overcome a beheading because it's instant death, but like a vast majority of other things that feature beheading as the one weakness to something. Totally obliterating the body would also work, but with how unlikely it is for that to come up I didn't mention it.
Vampires are not in this, I used them as an example of something from mythology that, as one version of its one weakness, must be decapitated. After all, some versions just have the stake holding them down instead of actually killing them. If vampires were actually in this they would work differently than sapient undead, but they are not.
You also have to die and be properly resurrected very recently to be a sapient undead. There are paths to longer lifespans that do not in fact involve dying and needing proper spells applied to you that are only going to be known by necromancers who are not well-liked at all. Creation of sapient undead is not reliable.
I'm going to be frank and ask you why you're still in this RP if the setting causes so many problems for you. You've nitpicked at nearly every decision I've made in regards to the lore and consistently started excessive arguments that are quite frankly wearing very thin on my patience. I've tried to be very civil and every time an argument ends you find a new thing to pick at.