I think the fact that multiple Endless persist after we shut off the terminals sustaining them—and whose dissipation is rooted purely in their own self-fulfillment—is proof enough that the Endless aren't being operated by some heretofore unseen AI. This is especially evident with Dreamborough's residents, who persist as voidsent-like beings despite decades of disconnection from Everkeep and Living Memory. Likewise, that they explicitly require living aether to sustain themselves, something that's been said of voidsent and sin eaters, but notably not primals, familiars, or arcane entities... I feel that's enough to say that the Endless are living beings, albeit incomplete ones. Like the Ea they lack physical bodies, and spend the bulk of their existence inside domiciles that preserve their incorporeal form. Like the Omicron they lack "the vital spark"—souls, I believe.

All that is irrelevant in the face of Living Memory being a system that devours life to sustain the Endless, resulting in an ever increasing population of Endless that in turn require even more death and destruction to sustain them. It needed to be shut down before it could destroy the Source, to say nothing of the Reflections, the Universe, or gods forbid even the Multiverse*. That the Endless don't begrudge this shouldn't come as a surprise—their self-defined purpose is reaching a state of fulfillment, which Cahciua, Otis, Wuk Lamat's entourage, and the WoL provide them every step of the way. It's precisely because of this need that Cahciua has us reactivate the fountains, and why she insists on stopping to smell the roses, so to speak, alongside her son in the final region.

*As an aside, what do you suppose happened to Everkeep in the 8th Era timeline, where Black Rose left the world of Hydaelyn nigh incapable of sustaining life for at least 200 years? The Key was still in the Source, so unless an Ascian helpfully delivered it to them it's unlikely that they could use interdimensional fusion to sustain Living Memory.