My Epic Games Store copy of the game stores savedata in the %APPDATA%\Playdead\Inside\Game2.sav file. This is on Windows 8.1 x64. I'm running the game straight from the exe rather than through the Epic portal.
Topic on Talk:Inside
Added an additional path for EGS to the page, the same path is used by EGS for cloud saves, as seen here https://epicdata.info/item/6fdb5feba66846cd8623a6d15ca68080 . The Steam/GOG/itch.io version should preferably be checked to see what path is the odd one out.