As OP, I've quietly tried every suggestion here. The closest to working is the one to change the Options to default to typing into Search and then off again, but I find it only fixes it for a bit.
Whoever suggested it was a "focus" issue nailed it. Because I've noticed that:
a) It always happens after I do something with the navigation bar. Right-click copy as text, type into there, copy from it, etc., and
b) After it starts, it happens with any of the toolbar buttons, not just New Folder.
Cause: What is happening is that once you click on the navigation bar, the focus is stuck there, and clicking New Folder or Delete or Copy or anything returns focus to the navigation bar after you click.
Workaround: What you CAN do, immediately, to make it go away (until you click into the navigation bar again), is simply click into the Search text box and then continue on with your Windows Explorer file options.
I wish MSFT would fix this, it's ridiculous how long it's been around. (The person cussing out MS a few posts above has also nailed it - how the f is this fing sh still a problem?)