tl;dr: try temporarily turning off your Time Machine backup if you encounter this disk space error in the App Store and seem to have enough free disk space.
I ran into this issue today and thought I would post the solution that worked for me. The situation: trying to download a 13GB app from the App Store. I kept receiving the "There is not enough disk space to install the product," even though I had 25GB free.
I moved files onto an external drive to free up 55GB of space (as reported by Finder), but I was still receiving the error in the App Store.
I looked under "About this Mac" > Storage to see if I was keeping any local Time Machine backups. Sure enough, there were 33GB of local Time Machine backups shown in purple.
I turned off Time Machine in system preferences, which eliminated all of the purple in the storage listing and changed my free disk space to ~44GB (yes, it decreased).
But when I tried to download the app from the App Store, it worked like a charm.