For a real mind-blow, check out the Antikythera mechanism. They think it was made around 80 BC. May have had around 37 bronze, meshing gears.
To answer your question, it’s really a matter of time/effort. Sure, we are able to duplicate precision better and faster than we used to be able to. But the precision itself has been there for a LONG time.
you are just underestimating how well humans can make precise parts. 0.1mm is easily visible by eye. people make lenses by hand to tolerances in the 10s of nanometers. we have had machining equipment that can hold single digit µm tolerances for over 100 years. in addition to this many of those watch parts were custom fitted to that watch and had tolerances adjusted to fit that exact watch
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