Very hard. And it comes at an outrageous price. Independent watchmakers usually go one of four routes:
1) Source a movement from a big manufacturer (eg; ETA/Valjoux or a japanese/chinese movement) and use it as is but design the case/dial yourself
2) (1) but modify the movement adding functionality, replacing parts, or refinishing it to your own standard
3) Designing a custom movement around specialty movement parts from a supplier like Jaeger LeCoultre. They make some of the trickier parts (gears, balance springs). They can also manufacture special parts on a swiss screw machine.
4) Going through a bespoke movement maker like agenhor. You tell them what you want and they have both the machinery to make many custom parts and source the rest from elsewhere. They also provide movement design expertise.
Actually machining the watch parts isn't the hard part... the tricky part comes in things like hairsprings and escapements which are made from sometimes exotic materials like silicon. Some tiny watch parts are made using electrical discharge machining which costs $$$$$$$$ as well.
Looks like a fun website to spend a hour or two. Thanks!
Regarding tolerances, your OPs article states that they were actually able to produce them before, but not at a satisfying quality. I don't know what a 'good enough' quality is, though. It's a good story nevertheless :)
It was only in 2017 that China joined the elite club of countries capable of making ballpoint pens. Is it that hard?
https://www.washingtonpost.com/news/worldviews/wp/2017/01/18...