you can clearly see that its fake because the clouds are exactly the same at 0:24 and the end 1:24 seconds

This does not make it fake. The time-lapse is constructed from individual still images animated into a sequence. At some point towards the end of the time lapse as the sun got further away / went behind the mountain, Anthony probably chose to add in some images from the beginning of the sequence, probably to create a satisfying loop for his animation - to give the impression of it recurring again, which of course in reality it would. I doubt he realized he would have to deal with flat earthers accusations when he did that - it was an aesthetic choice made a film-maker.

why not film it?

Powell is not trying to create videos that prove the earth is not flat, that is merely incidental. He is using his digital stills camera to make animations that capture the movement of the sun and 24 hour sunlight in Antarctica.

Filming for 24 hours straight, uninterrupted, is more complicated than you have obviously considered. It is obviously not possible with analog film. But even with digital, it is not simply a matter of leaving the camera running. This is due to memory, power and camera restraints - you can see some discussion about the complications here if you like:

https://www.dpreview.com/forums/thread/3735074

You need specific brands of camera that have no recording limit (many do and will just shut off after a certain time period - this is to protect the electronics from being destroyed by over-heating), multiple memory slots and/or sufficiently large memory cards, a constant power source etc etc - and there are added complications when filming in Antarctica not mentioned there - extreme cold temperature affects battery performance and digital camera performance - it's quite likely a digital camera will just crap out before the 24 hour mark - due to cold rather than heat. Digital cameras are not generally built for extreme use like that.