Success! Thank you all for your helpful troubleshooting. For the record, I found no WM_COMMAND 41007 in the debug log, and removing the keyboard shortcut did not solve the problem. This strongly suggested involvement of another running application, as you all have deduced.
It turns out the culprit was "
Quick Look," and closing it solved the problem. This is a program that allows the user to hit the spacebar in an Explorer window to see a quick preview of the file (like in macOS), and presumably it works by copying the filename and passing it into the viewer.
It is worth noting that file paths are
not copied when scrolling through a regular Explorer window with Quick Look running; it only happens when using an Everything window. Moreover, the Quick Look spacebar-preview feature doesn't even work from an Everything window, so I never suspected that there would be an interaction between the two programs. Also interesting that it obeyed the "double quote copy as path" setting in Everything, as noted.
Overall an interesting and unexpected result. I'm not sure if you would consider this fixable/a bug as far as Everything is concerned (it might be one of those things that would need to be addressed by the developers of both apps) but it would be great if something could be done about it. In the meantime, I might have to look into one of those clipboard-history programs to avoid losing clipboard contents. Thanks to NotNull, therube, and of course void for your assistance.