Have the exact same issue since origin forced me into the stupid EA app. I miss playing mass effect as it's a childhood favourite I like to relive from time to time. I Also own it through steam.
I have the same issue (also having it on Steam since release), although after several minutes of waiting EA app finally pops up this message with EC:10600:
It seems to be a save sync issue with EA app. At first I thought it has something to do with Onedrive syncing the entire Documents folder which contains MELE saves as well, but it had been doing for years without issue. No idea what has changed in the last couple of weeks to make EA app this finicky.
