In the series DARK, we are shown Claudia taking one single set of blueprints to her World and giving it to HG Tannhaus. He then uses those blueprints to make the Briefcase time machine of Adam's world.
Who then invents the time machine (the ball) of Eve's world? There were only one set of blueprints, how does one make two radically different time machines from one blueprint.
In short, who invents the time machine in Eve's world, and how?
There were only one set of blueprints
I'm not sure how you concluded that, but it is not correct. It's hard to make out, but Adam has blueprints for the golden sphere on his wall:
Left is the suitcase, right is the ball.
Whether this is a recreation or an original is unknown, as is how Adam came to possess the blueprint, but the point remains that there wasn't just one unique blueprint across both worlds.
Adam's and Eve's world have many variations on the same thing (often reflected in the characters): Helge's wound, Charlotte's hair, Elisabeth/Franciska's deafness, Adam/Eve similar stories, Wöller's injury, Martha's hair color, ...
It's perfectly possible for the golden ball to be a variation on the suitcase. You can even make out that the title of the two blueprints ends in "A" and "B", suggesting they are variations on the same design.
With the added feature of travelling across worlds - it's never explained how they developed that feature or if it was serendipitous.
In the series DARK, we are shown Claudia taking one single set of blueprints to her World and giving it to HG Tannhaus. He then uses those blueprints to make the Briefcase time machine of Adam's world.
That's what happened in Adam's world. But what about Eve's world? We simply don't know. In absence of a difference being pointed out, the reasonable assumption is that Claudia-B went to Tannhaus-B to get him to create the golden ball.
It's not unreasonable that the show skipped showing us essentially the same scene, but with a different blueprint, if it's not important to the plot.
