I think this may actually turn into a bigger plot point than it seems rn but it's all still personal speculation....
1. Before Barbara and Barbie were the currant soot producer (living battery) duo, how DID the manor meet the "essential soot output"? I think early on it's mentioned that Barbara produces so much that the adults don't need to contribute or something? (I'll look back later for the specific detail). But that just raises some questions: was there a previous soot battery duo? Or did the Shadows House originally TRY to streamline production to farm it from multiple shadows, but then came up with a process to create a "living battery" out of the children's wing to be more efficient? The way Edward is talking about Sara, how all he has to do is "fill her with negative emotions", and then she becomes Barbara 2.0. He specifically states he was "looking for a powerless," which implies that's a requirement for whatever process he's about to start with her. Makes me think of Anthony's "fragments of favor" and how he used it on the /powerless/ Margaret to jumpstart an insanely out of control soot power up. Anthony was watching her to make sure she would have the negative emotions to trigger the reaction. And of course, after a while the power up was actually quite painful for Margaret which is why she died. Meanwhile, we know Barbara's "seizures" are quite painful for her..... If the "fragment of favor" IS related to what Edward is going to do to Sara, then Anthony is missing a key component to the process since Barbara is definitely dying but it's been long drawn out. If true this all comes back to: why would Anthony, a human, need to be carrying around something that has the effect of significantly amplifying soot powers? He at least needs to trust whoever uses and needs it to last longer than Margaret if he's going to use the children as pawns to fight the adults. Personally, this makes me more skeptical of Anthony's claim to being (fully) human, and that it's all been an act to fool Kate (and the readers). Am I overthinking it, yes. But I'm having fun with this manga so it's fine.
2. More importantly tho, what DO they need the energy FOR? The Shadow House "runs" on soot power, but thinking more on it now what does that really mean? Up until this point they don't really go into the details for the mansion, they want the shadows and children to assume it's for like maintenance and utilities or something, right (and by proxy the readers). However, I'm gonna say I don't think they're using much of the soot that's being collected by Barbara to /maintain/ both the Children and Adult facilities. Think about the ridiculous amount of soot we've seen used on the WHOLE island itself that the towns get from the mansion shipped out via trains. It's literally marketed as a fuel efficient alternative to regular coal and made to seem like an infinite product when we know it's not and where it actually comes from. I don't think Barbara is single handedly supplying the whole island or anything either. But I suspect there's something else (most, if not all) of her soot is actually being used for. Like, really?, they're using Barbara as a living battery to make the UTILITIES in the mansion work every day? But they ship out the soot coal like they're never running out of the goddamn stuff? Idk, the more I think about this the more it keeps me up. Could there be something MORE messed up the Shadows House would use the "living battery" child soot production for? Knowing the cruelty and horrors of the Shadow's House so far, it's possible.