If you group paths, the shadow rotates with the path.
Problem with InDesign version 2026: The shadow in InDesign rotates with the path. The problem is that sometimes you want to be able to rotate a series of paths, even complex structures, but the shadow doesn't rotate with the path. This is a problem. The only solution is to avoid using the shadow tool. You can create shadows alternatively with other paths, or you can have to re-edit all the shadows once the paths have been rotated. As far as I'm concerned, this is crazy. At least make sure that if the paths are grouped, this problem doesn't occur!
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Mario Artoni commented
often create projects that I then rotate. Let's also say that this would have been a new behavior to point out to users. For layout reasons, I had rotated the entire document by 90 degrees... and then sent it to print... Luckily, I discovered a text error while correcting it on the rotated sheet... and I noticed that all the shadows were rotated... Danger averted... but it would be absurd not to warn of a potential problem given the totally different behavior compared to previous versions of InDesign.