So the question of where it is installed is kind of complicated. The whole reason I stopped being able to open the game is because I was having a lot of performance issues playing it installed on my laptop so I wanted to move it to an external drive, and I followed some instructions I found on reddit and probably did something wrong, because I wasn't able to open the game after moving the files to the drive and started getting the endless "verifying" loading screen. At that point I tried to move the files back to my laptop, thinking I'd just manually uninstall them, then change the download location for new downloads to the external drive and download them all again from origin. But when I moved the files back to my laptop I tried opening sims just to see if I could again, and I was still getting the endless "verifying" loading screen. Over the last two weeks of communicating with EA support I've tried deleting and reinstalling the files on the external drive and on my laptop, and no matter where I install them I still get the "verifying" screen that won't stop loading if I try to launch the game.
Just now I checked my permissions and you were right that origin and sims 4 didn't have full disk access, but changing that didn't let me open sims 4 with the files installed on my laptop. I then tried trashing every file listed in the link you sent me, trashing the old sims 4 files, reinstalling origin, and opening origin and reinstalling sims 4 on the external drive. The download is currently stuck on the same "verifying" loading pop up. Currently Origin has full disk access in my preferences, but I can't give sims 4 full disk access because it's not currently installed either on my laptop or on my external drive.
Ultimately, I would like to have sims 4 and all my purchased packs installed on the external drive, but I am open to anything at this point just to get the base game to open again, and then would be fine with figuring out how to get all the files on the external drive after if that is easier.