I built a completely new install, did an update and nothing else other than installing Brave using the command curl -fsS https://dl.brave.com/install.sh | sh from their site. (On arch, the script does pacman -Sy --needed --noconfirm brave-browser to install it.) Nothing else was added to the system. I did nothing to change the default settings for the DE.
I opened dolphin and created a couple test documents. I checked the “Desktop and Wallpaper” settings and “Layout” showed “Folder View”. I then tried dragging the documents from dolphin to the DE and nothing happened. It did not create the link, it did not bring up a menu.
I then changed “Layout” to “Desktop” and repeated this test. In both instances, the menu came up with options to “Add sticky note” or “Add icon”. I selected each option on each document and the options worked as expected.
Anyone who has read this far will recognize that this is pretty much the opposite of what I was experiencing as noted in the OP.
So, weird. I hate bugs like this…