Having the same greyed out saved games option and no autosaving feature (even though before the main menu screen the 'AutoSave for this game' shows).
Made an account so that I might be able to post some of the things I have tried in order to fix this, but has NOT worked for me. I have bought the game with the Epic Games Store and the first being uninstalling and reinstalling (multiple times and on different drives), and trying to verify the game files as well. As suggested by a friend, I had attempted to try taking the saved game folder "The Outer Worlds" and changing off of "read only" which did nothing because it kept reverting back to "read only". With this said while he was able to save his games no problem and have folders being made inside that "The Outer Worlds" folder for his autosaves marked accordingly. While in mine the only file i had in that folder was the achievement.dat . So at this point after many attempts of trying to get something to work, I was able to get his save file of his freshly landed character (only played for 1minute) and put that into my folder. From here I was able to "Load" a game and this character just fine, but STILL NO ability to 'save game'.
While I loved the few moments I am able to play the game itself smoothly, the inability to save a game fails at making the game being able to continued when you need to stop. So until this is fixed I am unable to even play the game with any enjoyment.