Ok so running the game from the 7DaysToDie_EAC.exe link I was able to start the game and play, however my logs did not update. I just tried running from Steam again and it still won't launch but my launcher.log did update. Here is the pastebin for it
https://pastebin.com/1ePU84iA
My output log however did NOT update, it shows the most recent file is from 5/10/2022