Not a native English speaker here, my focus stopped at the subtitle "Robotic private spacecraft touched down about 250 miles from its intended landing site on Thursday". It feels odd to read "robotic private spacecraft" instead of "private robotic spacecraft" but I can't explain why.
In this case, "robotic" and "private" could be similar enough in category to be confusing. In the Order of Adjectives[0], "robotic" is in the TYPE category, near the bottom of the list, and "private" seems to fit in that same category at first glance. By that interpretation, either "robotic private" or "private robotic" works.
What if instead of "private" it said "Californian"? That would make it an ORIGIN, and "Californian robotic spacecraft" becomes the obvious choice — otherwise, you'd think they were talking about a spacecraft belonging to robots from California. ;)
So if we interpret "private" as an ORIGIN, your "private robotic spacecraft" sounds better. That would have been my choice as well.
[0]: https://dictionary.cambridge.org/grammar/british-grammar/adj...