Why, when crossing staffs, does Dorico put the staccato dots above the notes? I’m afraid I don’t get it.
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OK, I found that I can force it to the notehead side in the “articulations” property panel, but I don’t know why that position would be default.

In contemporary practice, articulations are usually placed on the stem side when there are multiple voices on a single staff. See p. 116 in Gould’s Behind Bars. Yours an exceptional case, since the top voice moves between the staves, but I think that Dorico is probably following Gould’s “rule” literally. In this case, placing the staccatos closest to the notes seems fine to me. In earlier times, articulations were placed more freely depending on the situation.