Ok, I saw the stuff you want to make :
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Actually, I didn't watch long but since it doesn't move a lot, a couple of power windows would be enough (one to exclude what the sky is not part of and another to select it specifically), then... whatever may satisfy you (like Hue tweaks or color boost + offset etc...).
If the cam had regular sudden moves but keeping specific landmarks always in focus (like buildings or trees), you may need to track before, than use one of the more relevant technique.
Btw, sometimes, the more basic works great, therefore the "-100 strong trick" in the classic stabilizer which consists in replacing the sky (not only changing the color of the real one) and make it follow the moves of the cam to stick with the rest can resolve 80% of your needs. You'll probably find tons of tutorials for that

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