Uninstall and reinstall game

@Sapphir567  If your computer is being wiped, as in the current hard drive will be completely erased, you don't actually need to uninstall anything.  Steam and Origin will read that Sims 4 isn't installed, there will be no leftover registry entries to get in the way; it'll be as if you're installing on a new computer.

If you do want to uninstall, telling Steam to uninstall the base game will also remove all the packs.  Uninstalling Origin is done separately and doesn't remove installed games.  Again though, you don't need to go through the trouble.

Once you have your computer back and have reinstalled Sims 4, launch the game once to make sure it works.  Then copy the contents of your old saves, Tray, Mods, and Custom Music folders, not the folders themselves but the files inside, to their respective folders in Documents\Electronic Arts\The Sims 4, and your content should all appear in-game.

By the way, if you haven't already, it's a good idea to save zipped copies of the folders, particularly for mods.  Some players report that .package files moved to an external drive and then back to an internal one stop working properly.  I believe this is due to the format of the drive but haven't tested.  Point is, it's an easy problem to avoid: right-click on the folder still on your internal drive and select Compress, then transfer the .zip file to the external.

So I zipped all the individual subfolders that were in my Mods folder (Hair, Clothing, etc.) - I figured it would be easier to unzip and organize, and transferred them to the external hard drive (I have a 1 TB Seagate). So basically when I double-click on the zip, the folder appears, and when I double-click on that, I see its contents. I also compressed my Tray, Saves, and Custom Music, and transferred them all over as well.  Not sure it's best to use an external hard drive or Google Drive, but I'm running out of room on Google so I figured this was best.

Would have it been better to compress my ENTIRE Mods folder, subfolders and all?

When I reinstall, all I do is unzip the folders (I'll probably do one by one by copying them to my desktop) and copy them into the new folder? For example, I unzip the Accessories folder and just transfer that unzipped folder into the new "Mods" folder?  And with the Tray and Saves (which are easier since there are no subfolders in there) all I need to do it just copy the individual files and put them into the "new" Tray and Saves folders, correct?  What about the music?

The screenshots I just saved separately - they aren't terribly important.

@Sapphir567  The way you've done things should work fine; my point was that the files should be zipped before being transferred to the external drive.  And using an external is perfectly fine, certainly not worse than using a filehosting service.

When you're ready to use them again, transfer the .zip files to your internal drive first, then right-click and Extract, and copy the files, not the folders, to their proper locations.  You can create new subfolders if you want, but it's best to use new folders rather than the ones you get when you unzip.  I mean, those folders are probably fine, but not using them eliminates one more potential source of error.

So if I understand correctly, I can transfer the zip files to my desktop from my external drive.  I can extract those zip files so I have the folders I started with.  Then, instead of dragging that folder back into the Mods folder, I create a new subfolder in my Mods folder ("Accessories" or something like that) and just drag all the individual files from the old folder to the new one, and then delete the empty folder from my desktop.

@Sapphir567  Exactly.  And like I said, this extra step may not be necessary, but it's always good to be extra careful.