Well, this is interesting. Today, the computer did not turn itself on. Too early to tell whether the issue has been addressed, but will watch it for a time to see.
On my (so-called) desktop systems (actually, under-desk tower systems), I use wireless USB mouse, but PS/2 keyboard. The reason is that I love to be able to turn the system on by just touching a key on the keyboard, and Wake-on-Keyboard only works with PS/2 keyboards, not with USB keyboards. So, Wake-on-Keyboard is one feature that I hadn't turned off. But the keyboard is on a drawer which slides under the desk when not in use, and so somewhat protected (as from falling objects, for example); and, there is no one here that would be pressing keys. So, I didn't suspect that feature.
Yesterday, I turned that feature off. And, while in the BIOS Power tab, I saw something else enabled, which is labeled High-Precision Timer, which I turned off as well. Can anyone say what that timer is for? And, if the issue proves to be solved, which of these two features would you suspect?