hy what are photography threads ?

is not only hardness or angles, but more edge sharpening and resistance, thus what matters more is final tool condition

i have crafted reamers, centers, threading holders for indexable inserts, etc

once you start wish to diy, is all about the level of quality that you wish to achieve :
... something low : simply do whatever you wish, and what you do is what you get
... high quality : get material for tooling, rough, heat threat, then grind; contact a local tool manufaturer/sharpner, so to only quote the grinding after heat treat, and discuss with him geometrical conditions that your part must met before sending it to him

about rake angles, i can tell you that there are tools with non standard angles that still work; for your exact application, i could contact someone and find exact technology details, but until then, i will take a look inside a manufacturing catalogue for taps and dies, that, lucky for you/me, i have in house : voila, that u shape is not an u

the od of the tap is not a revolution shape, and that groove is an u with curved sides; from this consideration, you could simply deliver a revolution shape with a normal u groove to your tool sharpener, and he should take care of the details / kindly