Update that may help others: The CMOS battery is definitely not a CR2032 in the XPS13 9360. It's less than half that size, is covered in black tape, and has cables connecting it to the board. I didn't have a replacement, but I did disconnect it, reconnect it, and then put everything back together once more. That required a round of BIOS updating (time, date, and downloading/installing the most recent one again from Dell). Good news! So far, the machine is now behaving the way it's supposed to. It re-awakens after going to sleep instead of only re-awakening from a full shutdown. I you don't see another comment from me to the contrary, this fixed the problem. Just to be clear, I did not replace the coin battery in any sense other than disconnecting and placing it back exactly where it was; I replaced the main battery with a new one of course. Installing a new coin battery seems a good idea though if I can find a reliable replacement.