Typical "Sasuga <insert name here>-sama", I love itMisunderstood on practically every turn
K not sure if they are going to explain this further on in the manwha but, in the novel she explains the business plan further to the audience. The design of the scalpel is the first step next was making them out of stainless steel to help reduce infection (thus promoting the attraction of said scalpel to surgeons.) . And while you're right there aren't millions of surgeons there are probably at least 20-50 thousand (America for example has around 150 thousand) . If she literally has 100% of the market share from superior technology than that's plenty of money to live off of even if she only sells 5-10 copies to each surgeon every year (because even with their technology tools will degrade with use). Plus unlike business in the modern world where a "knock off" brand can be made with some basic skills and analysis, imitating an object made by the royal family without permission would soon find you on the business end of an executioner's axe so yeah she would literally have the market all to herself for the entire country.That's not what a scalpel looks like... The hole in the blade is where it attaches to a handle, and the blade is therefore disposable, it isn't supposed to be attached at the base.
Also rather than blacksmithing steel without modern techniques for scalpels, obsidian would be a much better material as it is sharper, which is the most important thing for a scalpel.
Also for this kind of time setting the number one danger of surgeries isn't a surgeon botching it, it's infection. Introducing germ theory and sterilization techniques would be far, far more effective at reducing mortality rates. New scalpel designs would have a marginal at best improvement for surgery success rates since this country already has pretty decent technology for blades. Also how is this supposed to even make money? It's not like you have millions of surgeons without access to scalpels.