I wanted to know how HDR would be useful for fast movement as I want to look into cameras that will move through regions of bright light and shadows and so, I want to see how I can make the footage more clear rather than get bland too bright and too dark components largely in the video. I want to check how action cameras implement such huge dynamic ranges. I'm a beginner and am slowly learning, so I might not have understood this right, but please help
There is rarely a direct relationship between HDR, or dynamic range in general, and motion artifacts. There may be an indirect relationship when trade offs are made for transmitting or storing the increased dynamic range. A specific implementation might reduce the frame rate or increase the compression in ways that introduce motion artifacts.
If you see the term "HDR" applied to cameras (vs. display technology), it's nonsensical market-speak.
The metric which does describe a camera's exposure latitude is its "dynamic range," and the unit of measurement is "stops" of light. An expensive cinema camera like the Alexa mini (which is probably too heavy for consumer grade hobby aircraft) records 14 stops of dynamic range. A Blackmagic Micro cinema camera, which is closer to the size of a GoPro records 13. GoPro themselves don't advertise this number. But for practical applications like the one you're describing, it doesn't matter.
The reason dynamic range is important to a cinema camera is that cinema cameras don't use auto-exposure. Auto-exposure tends to cause abrupt, mechanical changes in image brightness of which a Director of Photography has little control.
Action cams, on the other hand, must adapt quickly to changing light without user intervention. So for them, fast auto-exposure is a necessity. Since they change their exposure rapidly, and autonomously, the latitude of dynamic range they can capture per single frame is less relevant.
To my knowledge, there is no codified metric for how well an action cam's auto-exposure performs, so I would look for sample footage and judge for myself.
Now, HDR as it applies to display technology is another matter entirely, and higher peak nit values will translate into a better viewing experience. Cameras have always been able to record a wider exposure latitude than displays can reproduce, which is why an "HDR" camera is nonsense -- they're all "HDR."