It isn’t clear to me whether The Thaumechanical Man is science fiction or fantasy. It doesn’t fit cleanly in either, but neither does it bridge or mix the two the way, for instance, Piers Anthony’s fiction does.
The fantasy/sci-fi division is an old argument, often centered around the two strongest known cases: Star Wars and Star Trek. In Star Wars, the story itself could just as easily be told in a world with horses and swords and magic. The technology is part of the scenery, not part of the story. In Star Trek, the stories generally revolve around warp drives and phasers and transporter beams.
This quality works in the other direction, too. Case in point: The Warlock in Spite of Himself. In that series, what they call magic is actually telepathy and telekinesis, and the main character is from a star-faring society, and the plot line revolves around him figuring out how it all works. That one’s cleanly categorized as sci-fi.
It confuses things that neither Panthropolis nor the Third Empire feel like they have a higher level of technology than we do. Panthropolis is slightly more advanced than our world, but the time spent in researching alchemy and thaumaturgy have leeched from their research in chemistry, telecommunications, electricity, and a few others. This confusion clears up a lot when we get to Hell, as the Hellians have a tech level somewhere between Expanse and Star Trek: Enterprise.
A clear issue is the existence of magic. Is it even possible to write science fiction with magic? Of course it is. In Dune, spice basically grants magical powers. Telepathy and telekinesis are endemic to sci-fi, but I think that “it’s all just psychic powers” is as tired a trope as “it was all a dream.”
For this issue, I’m going to invoke “in the real world, magic is just a technology we don’t understand.” Electricity was once magic. Nanosurgeons would be miraculous to us. When the technology involves laws of physics that we don’t even have access to, you have to call it magic even if it’s as rudimentary as banging two rocks together. However, if you define it strictly enough, you can treat it like a technology. My goal with magics is to be able to describe each of them mathematically, if for no other reason than to reduce inconsistencies.
How the FX are accomplished, however, is all window dressing. What really matters is the story. Could the story be told if it took place in a fantasy setting? Sorry, no, that’s a red herring. I don’t think we’ve effectively established that it isn’t actually a fantasy setting, so this perspective doesn’t work.
You could ask if the story revolves around understanding the implications of the technology, but that doesn’t work, either. Most books with a rigorously detailed magic system revolves around the workings and implications of it (Raymond Feist, Lawrence Watt-Evans, Brandon Sanderson, et.al.).
It all circles back around to how you perceive the tech/magic divide. At the bottom of it, I wrote this conundrum into the story with my foundational assumptions about the world. Any magic, if sufficiently reduced to practice, is indistinguishable from technology. Thus, fantasy becomes indistinguishable from science fiction. If I did it right, this question should be unanswerable.
Alas, this leaves me with a dilemma. I don’t know how to categorize it, but Amazon needs a category, doesn’t it? I picked science fiction because my writing style is more resemblant of Heinlein and Niven than McCaffrey and Tolkien. Maybe you can help me out. Where do you think it belongs?