I needed to reformat my external hard drive where I store my backup files. Although I succeeded in exporting all 15,000 files, they did not export with their associated folders. Instead, files are now stored in numerical order
Export has nothing to do with Backup and a System Backup has nothing to do with LR. To avoid confusion, are you trying to export all of your cataloged image files, Or are you trying to backup your critical user files including those required by LR?
First, there is no reason to export all of your cataloged image files. This is a fruitless effort as you can export individual image files from LR any time you need to use one for social media or web or print.
Second, you need dedicated backup software to manage all of your critical files in a location where these might be recovered individually or as a group when your Hard drive fails or when you do something stupid and erase or write over a critical file. Critical user files are all files that you need to access or preserve. These can include image file, your LR catalog file, Word Documents and spreadsheets.
You Apple OS ships with TimeMachine that provides excellent backup capabilities This free app is probably the first place to start for meeting your backup requirements for a local backup source. It does not protect you for catastrophic events that might destroy your home and your home network including your computers and you backup hard drives. There are other back up apps that can protect against disaster.