Interesting, but your screenshot is not really helpful. Use this tool to see what process owns this window. https://learn.microsoft.com/en-us/sysinternals/downloads/process-explorer

I'll give it a try, but the window doesn't usually stay around very long. It also doesn't have any visible text, so I don't know how I'll be able to pick it out of the list of processes.

You just need to open process explorer, then click and hold the black x from the menu bar, then move it over the window, and then let go of the mouse button. Process explorer will then show you the process for the windows. see screenshot

Thanks, although I'm using dark mode on my pc, so it's a white "X".

It definitely looks like a Firefox window. When Firefox is set to restore previous session windows and tabs, I think a blank window appears for several moments while Firefox processes the session history file, before it shows what you are expecting. But at least in my case, I don't think it's on top of anything.