I'm downloading SR2 and the store page says it's 5,8 GB but the download says 13 GB. What ?

How are you downloading the game? The store page will be for the GOG installer, which will likely have compression in place. But if you are downloading via GOG Galaxy then that downloads game files directly, so the compression may be different (if there even is any). Note that the game page also says it needs 15GB hard drive space, so that would be the required space for the install (and possibly also any swap space), which is more like the download size you are getting.

I'm downloading via galaxy. That makes sense but it's really confusing. Also, there were some instances of downloads that came up with the normal size (5.8). Strange behaviour. I guess I'll skip downloading until galaxy is more finished.

Yeah, completely ignore what the store page says, you're going to need about 11GB of space to actually install the game. I have no idea why the numbers are so off.