I am a scientist (a chemist, to be precise) but never in my scientific career have I come across a Royal We—not in English and not in German.
Most journal articles I read are full of we. But these articles also tend to have between two and ten authors. While it is assumed that one author did most of the work (usually the one listed first) the text is phrased as if all people were doing the work. To a certain extent that is justified, because the PhD student doing the lab work will give their supervisor frequent updates and in return frequently receive suggestions on what to do and how to do it. Thus, the we in these articles is the collective of authors addressing the reader(s). In German, wir is appropriate for the same reason.
In dissertations or other theses, it is slightly different as there is one principal author who compiled the text. In this case, I is the most common personal pronoun. We is sometimes but rarely used if a certain experiment was undoubtedly a group effort. This extends to the PhD student’s defence where most sentences are phrased as I-sentences (but e.g. publications are mentioned as we published X). The same is true in German: My dissertation mostly uses ich, rarely if at all wir.
Finally, in textbooks and the like it is typically a single author writing to their readers. Nonetheless, they tend to use we a lot. This, however, is again not a Royal We but rather an invitation to the reader to follow the chain of thoughts or the maths or mechanism or whatever together with the author. The same form is typically used in lectures where the lecturer expects the students to follow and expand the lecturer’s thoughts and expressions on the blackboard/slides. Again, in German this is wir for the same reason and not royal.
In languages that distinguish inclusive and exclusive we (the former including the listeners/readers, the latter excluding them), journal articles would thusly be phrased using exclusive we while lectures and textbooks would use inclusive we.
The above notwithstanding many scientific chemical texts are written in an unpersonal passive voice to keep the chemistry in focus rather than the authors. I feel that German may be using the passive voice slightly more than English to depersonalise science. Thus, especially in the experimental section it would become:
Methode X wurde verwendet.