whatme, I have directed you to sources which explain how physiological changes during lactation (and pregnancy as it happens) enable mothers to produce X calories of milk without ingesting X calories themselves - it's not magic, it is physiological, and it is the result of changes in the way metabolism changes. Please read them.
Tiktok, with respect, you misunderstand what your own papers say. They are merely saying that the metabolic efficiency improves. That does not mean mothers need less energy in than they give out, it simply means they need less extra in to get the same amount out, than they did before.
All - and I mean ALL - things in this universe, need more energy in per unit out, there is nothing that is even 100% efficient - and certainly nothing that needs less energy than it gives out.
Which, back to the orginal point, is why BF is not "Free" - whether you put the energy into the mother or the child, it costs you money. The cost of a weeks' worth of formula is about £9 (assuming a big tin lasts about a week), the cost of a week's worth of those calories in the UK is about £7 from the shops, give or take a few £ either way depending on whether you get it from coke and crisps or organic cabbage (the better the calories are for you, the more expensive they are - which explains a lot of the obesity epidemic, but thats for another thread....)
The body will find the calories it needs to feed the child, from fat or food, but it shuts even that down if the mother is at serious risk.