According to Wikipedia, the highest wind speed not related to
tornadoes ever recorded was 408 km/h. But I am wondering, what is the
maximum theoretical wind speed possible here on Earth?
The simple answer is "about the speed of sound".
The reason for that seemingly simple answer is the definition. It may seem like "speed of sound" has to do with, you know, sound. But in fact it doesn't, it's an underlying physical effect that just happens to apply to sound, and everything else happening in the air.
The physics has to do with the way the molecules in the air move. If you could look at them super-microscopically, you'd be surprised how fast they're going, on average about 1000 mph. However, because there's so many of them, they generally don't get very far before bumping into another one. Not far as in "about 65 nanometers".
Now one can imagine a situation where you have a vacuum on one side and normal 1 ATM on the other. So in theory, the molecules could move at about 1000 mph into the vacuum. But that would only be true if they were all moving in the same direction. In fact, some are going 1000 to the left and others 1000 to the right. If the vacuum is on the right, the ones moving to the left have to bump into someone before they turn around and start moving in the right direction. Once again, that all takes time.
So with all these molecules constantly bumping into each other, the net speed of a disturbance is slower than the motion of the individual molecules (think about the collection's overall motion). And that is why sound is about 700 mph instead of 1000.
Shock waves are another issue, but you did specifically remove "artificially created conditions".
Now of course, we're talking about a local effect, a relative speed - that is what wind is after all. If the entire atmosphere is moving at some speed then the speed of wind within it can be that much higher again. After all, the air is moving about 1000 mph at the equator, but the relative speed is zero.