I recently visited a friend's house, and I downloaded Papers, Please onto his Mac through my Steam account and let him play the game for a while so he could see how great it is. Unfortunately, when I got home and opened up the game, all my saves were gone.

I have checked C:\Users\Aidan\AppData\Roaming\3909\PapersPlease and all my save files are still in that folder. But for some reason the game does not see them and thinks the folder is empty.

I do not understand why this is happening. I made sure to uninstall the game from his computer and everything. If anyone could help me fix this issue, that would be great. Thank you

Well, since it seems you used your Steam version of the game, I think it would be better if you asked this question in the Steam forums, rather than here, since there's at least one major difference (mandatory client with cloud saves) between Papers, Please on Steam and the same game on GOG.

Welcome to the helpful community that is the Steam Forums.