Used my external hard drive as backup and now I can't see files that were previously there
Carbon Copy Cloner makes a clone of one entire disk volume on another disk volume. In other words, it duplicates the source disk on another volume, replacing whatever was already there.

A safer method would have been to use the drive as a Time Machine disk, which would then backup everything to the external drive, but keeping existing files in place.

If you can indeed recover all your files using Data recovery software, then you should go ahead with that. It is 'not easy' for you to do it yourself, as you would have to write code to read entire disk data blocks and work out where files begin and end (because they lack the catalog entry that the Finder can use to display files).

It is essential to have a second copy of every file that you want to keep, on another device, exactly to prevent situations like this.