Thank you very much for the info!
I looked around a bit and I think I finally found it! It was obviously something very simple: my game was set to “free with a paid file,” and by switching it to “paid with a free file,” the section dedicated to a demo appeared.
I'm still a bit disappointed that I can't leave it as free, because my vision was closer to having a demo version offering all the features of the full game, but with a paid DLC-like option for the two additional levels. I know this will probably have an impact on the stats. But well, the important thing for now is that people who already claimed it can download it properly.
After the end of the promo, I asked one of my friends who had downloaded the game during that promo to check whether he could still re-download it, and it seemed like he could.
But you're telling me that this is not the case for you? That you claimed the game during the promo, and now that it has ended, if you uninstall the game and try to reinstall it, you no longer have access to the full version?
Could you confirm that you claimed it for free during the promo and that you can now download the full version without any issue? I just switched to the "paid with free file" mode.