Recover deleted folder from user/library

It depends whether the remaining files you have are from an encrypted backup.

It won't be feasible to read your backup data if you have an encrypted backup with no Info.plist, Status.plist, or Manifest.mbdx files

However, if your backup wasn't encrypted, it will be possible to read that data. You'll find that whilst the filenames are unhelpful (they're SHA-1 hashes of the file's internal path), the file contents easily readable. It's only the filenames that'll be lost.

If you're looking for images, try renaming a bunch of the files to have .JPG extensions, and see whether Windows Explorer or macOS Finder previews them for you.

There are a few approaches for digging into what's there in bulk. You mentioned using iPhone Backup Extractor, and there's a guide on how a use "Bulk Rename Utility" to read backup data when in this situation.

Data Rescue is a long time favorite for undeleting files. It is not free, but you can download a free trial to see if the folder and files can be recreated before deciding to pay for the software or seeking professional recovery.

Similar to Windows, OS X doesn't wipe the files but instead marks the directory entries as free. As long as the files do not get overwritten (say you powered off the Mac immediately after the error was performed) you should get most of the files back. It all depends on chance that the system didn't overwrite the files as part of the normal shutdown process.