@Kayriari There is a much newer graphics driver available for your card; yours is from 2012. So it may help to install it.
https://www.nvidia.com/Download/driverResults.aspx/132844/en-us
However, since the standard version of Sims 4 is working and the LE is not, I'm not sure that would fix things. I'd rather see info from the Reliability Monitor first. After trying to launch the Legacy Edition again, hit Windows key-R and enter "perfmon /rel" without quotes. You'll see a list of errors and updates, with a column for each day. (Today is all the way on the right.)
If you see an error from when you tried to open the LE, click "View technical details," then copy the information and paste it into a text document. (Notepad is fine.) You can just copy and paste the info into a post. Sometimes the Reliability Monitor doesn't update right away, so if you don't see any related errors, be sure to check back an hour or two. The timestamp on the initial chart can also be off by up to an hour, so that's not an entirely reliable metric, but the one within the technical details should be accurate.
When testing, please run both Origin and the game as an admin: right-click on the Origin shortcut and select "Run as administrator," and do the same for TS4.exe or its shortcut. Make sure Origin is set to run the LE as well, since it will override the shortcut you use and open the version of Sims 4 saved in its settings instead.
The contents of your Legacy Edition user folder look normal.