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Solved!!!!!
I have confirmed my critical battery level action suspicion I described before. To test it I set my critical battery level higher and unplugged my PC to run it down to that level. As soon as it reached that point, the blue "Locking" screen popped up and it went into hibernation just like it's set to do. There was also another very quick notification screen/message but I'm not certain what it said. I think it might have said something about critical battery level but, again, I'm not certain. I am 100% certain that I saw the mysterious "Locking" message on a blue screen exactly as I'd been seeing it before all those times.
So anyone else who is having this same problem, you most likely have a really old battery that drains super fast when you're working your PC hard and using a lot of energy. Or your battery may be malfunctioning but leading to the same issue. It's draining so quickly there's no time for the other power level notifications and it's going straight to the critical battery level action.
There is another thread somewhere else where the Windows "expert" states that he is not aware of any screen or message that says "Locking" in Windows 10, which we now know is incorrect, and that is probably causing a lot of confusion for those of us that are experiencing this rare issue. I even noticed that the font for this "Locking" message was the same Windows font we're so familiar with. And since I read somewhere else someone was having this same issue on a Dell laptop, we can be certain that it is indeed a function of Windows 10.
Now that I've confirmed it myself, I can stop worrying about malware or a virus causing it. That would be a very weird thing to be causing anyway since there's no other issues related and I can always restart, or bring out of hibernation, my laptop no problem.
Well, I hope anyone else that's having this same, strange issue reads this and finally finds some clarity. If you do happen to read this all and changing the battery does solve the problem, please post a response here if you don't mind. Even though I'm 100% now that I've found the answer, I'd still like to get outside confirmation and also know if my efforts have helped anyone else. This is such a rare, weird issue that even the Windows experts have been stumped. It would be great for my ego to know I did, indeed, solve this mystery.