Looking up the etymology of the word "manufacture", it's from Italian/French/Latin words for "made by hand", weirdly enough (at least, according to my lazy googling.)
I say "weirdly enough" because you contrast the difficulty of manufacturing vs. making things by hand. Originally, they were the same thing, apparently (and maybe too obviously, as everything was "made by hand" in antiquity, but I found it interesting, from a kind of "word nerd" perspective)
I think the industrial revolution changed the word's use by changing the context in which ordinary speakers ordinarily use it.
In this specific case, the OP mentions factories...and that's another word that doesn't mean what it once did when "factor" was a common term for an occupational category.
"Fabricate" is another interesting term that might be useful in this context as it suggests a mechanized workshop..."workshop" seems to fall into this space too. To me it seems scale is much of the difference between factory and workshop. That scale is probably industrial.
I say "weirdly enough" because you contrast the difficulty of manufacturing vs. making things by hand. Originally, they were the same thing, apparently (and maybe too obviously, as everything was "made by hand" in antiquity, but I found it interesting, from a kind of "word nerd" perspective)