Just to clarify, if you download a fresh Mods Framework
from here, unzip and put it into place, and clear (delete) the five cache files on the top level of your TS3 user game folder in Documents, does your game not start and load the two small, sample mods that come with it?
I am
NOT the expert here, but I think some players have had to reinstall their games from the beginning after transitioning from Origin to the EA App to get mods working again. But don't do anything drastic until a player with actual experience on that platform confirms.
What is always safe to try in the meantime is a fresh TS3 user game folder. Move the current one out of Documents (or rename it) and a fresh, no-content one will spawn to take its place. Your content and saved games, etc. will still be safe in the pulled out folder. Can you set up the Mods Framework properly on this one?
Note that during all this testing, the game will certainly crash on startup if it reads the MC Progression module but StoryProgression (the SP base mod) is not present. Even those of us who know this inside and out, or the thing with Cupcake when the bakery set is not present or loading, sometimes make this mistake while troubleshooting with handfuls of mods here and there as it's so easy to do by accident.