As stated in the subject of this e-mail, the command MathematicaScript became wolframscript in the newer versions of mathematica. To make ob-mathematica.el work again with newer versions of mathematica simply replace all occurences of MathematicaScript with wolframscript in that file.

An extra comment. Wolfram made it's Wolfram Engine freely available for developers. And I guess it can be used to, for example, produce Mathematica Plots (or graphics) in the jupyter notebooks using the Wolfram Language kernel for jupyter (I am not sure because I have a licensed Mathematica version and I guess my jupyter is using that kernel to get the graphics). Would be great to have such functionality working in org-mode (with-babel). Unfortunately I am not a developer. But someone else might like the idea too.