I might agree if the longsword recipe wasn’t included in the Ye Old Scottish Bakery book that teaches cooking and haggis.
“You can make this so you should be able to make that” isn’t accepted as justification. It’s entirely possible the medieval weapon recipes in Ye Scots Beuk o Cuikery should be removed instead.
Without actual instructions on the tools and methods involved, illustrations of a sword would at best let you make a “sword-like object” - it looks like a sword, but doesn’t function anywhere near as well as a real one (kinda like how characters with gun and fab skill can make pipe rifles - they know the basic mechanics of a gun and can extrapolate from that to make a gun-like object, but don’t have the tools or know-how to make anything better). It wouldn’t be as hard as a real sword, or as tough, or as balanced, or as light. Even if you know the swordsmanship techniques and have a picture, you could never learn the forging techniques without a forging book. You wouldn’t know how much metal to use, or the alloy composition needed, or how to make the alloy, or how hot to make the furnace, or how to use the furnace at all, or how to hammer out the blade, or the dimensions needed, or how to quench it (or even that quenching is a stage in the forging process), and so on. It only gets more complicated with the Japanese swords, which are composed of at least two different steel alloys with different compositions that cool and contract to different extents, creating the signature curve.
And if I know how to swing a sword I damn well know what I want to make, right down to the handling characteristics, distal taper and differential temper
No, you wouldn’t. If all you have is the swordsmanship book with vague, non-technical pictures of swords, you wouldn’t even know what a distal taper or differential temper are, or how to control them, much less how to refine them.
Real life smiths don’t just learn from pictures and a pipe dream. They learn under a teacher for years (or a library book for a few days, I guess). Then they refine their work from that pre-existing knowledge base. If you want to replicate that knowledge from scratch, how many prototypes will you have to destroy just to create a sword-like object? And then how many broken, bent, or dulled blades will it take to realize you have the alloy composition wrong (if you figure out that’s the problem at all), and how many more iterations will it take to get the composition right? If you’ve never held a real, properly forged sword before, how long will it take to figure out the balance is wrong, or the blade is too thick, or the tang or temper is wrong, if you even realize these things at all? In real life, it takes days to actually make a sword if you already know how; the game is very generous when it comes to forging time due to previous limitations of the crafting system, but that can change now that you can put down a crafting project and pick it back up later. I would give it months to learn how to craft a proper medieval European sword from scratch. Learning how to forge a Japanese sword from scratch is infeasible.