You can disable snapping, under Preferences, in the Cinnamon System Settings app > Window Tiling settings > Enable Window Tiling and Snapping > off.
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Thank you for your answer. I should have mentioned that I had already tried that.
Yes, this disables window snapping to screen borders, but not the strange grid behaviour when moving windows with the Shift key pressed.
Do you experience the same behaviour on your machine?
I can confirm this behavior on my machine. And after a (far too) long internet search, I think it might be connected to this Muffin bug report from 2023.
I checked every single setting window and tab and scoured the gsettings with dconf editor and as far as I can tell, there is no way to disable this strange window snapping behavior when dragging a window with SHIFT held down.
Of course, the fact that people keep confusing snapping with tiling did not help in my search.