I don't know anything about moon pictures, my best attempt was not great
But how did they composite 81,000 images without worrying about atmospheric lensing distorting the proportions as it moved across the sky for 4 days? Is it just negligible?
They didn't. What they did was take 81,000 images and then filter through, them taking the best images of each region of the Moon and then averaging and compositing those.
It isn't 81k images stitched together. It's 81k images taken in the hopes of getting enough with perfect clarity to create the composite.
The Samsung moon actually just makes up a plausible looking moon, which is hilarious given that the moon essentially doesn't change, so they could have just overlayed reference images. Instead, you get features on the moon that don't exist.