Hello @Florian,
I've narrowed down the culprit; the problem lies in my fb2k installation.
I'm using both the SimPlaylist and Facets plugins for foobar, and in both playlist viewer windows is where the issue manifests. In the standard Playlist View drag-and-drop works perfectly fine.
Since these plugins haven't been updated since 2011, I won't be asking for a compatibility fix from your end, nor will be expecting one.
Thank you for your time. 
EDIT: this thread is now closed, so no new replies are allowed, but for future readers here's an update:
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3.28c (2025-02-10)
- CHG: added support for writing covers of type Artist, Media, and Icon for MP4 via Nero tags to improve compatibility with other apps.
- CHG: moved configuration options to top of Tag-Panel context menu. (#67393)
- CHG: added workaround for drop sources that don't support the link drop effect (e.g., iTunes). (#67363, #67368)
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The drop sources workaround also fixed the issue in fb2k when using those specific (outdated) plugins.