Ok, I found the Save folder. Clicking on "ME1" shows me a file named "Launcher_Profile" and a folder named "PROFILE". Inside this folder is a file named "GamerProfile.pcsav". That's all there is in the Save folder. Right clicking on Mass Effect Legendary Edition doesn't seem to do anything on the EA app. Right clicking it on Steam does indeed give a list of options, but not the ones you've mention. There is nothing about Cloud Saves that I can find.
There are no cloud save functions, besides the automated you encountered, build in EA app yet, so my guide was for Origin.
https://www.dm.origin.com/download
If you don’t have it on your system anymore it is however unlikely that Origin will be able to restore the last save.
