Is it possible to re-organize my Catalog using the 'Capture Date' of every photo?

I have mistakenly duplicated, I believe, several thousand pictures in my catalog by accidentally dragging one folder to another. I believe the pictures were copied rather than moved because I am now seeing many messages about potential duplicates, but I'm not sure.

Lightroom only performs a MOVE. It never performs a COPY.

Is there a way, other than manually going through all the pictures, to reorganize the catalog and hence the pictures on disk so that each picture is in their proper folder based on thier Capture Date?

Yes, but you probably won't like the answers. You could, of course, manually move the photos to the correct folder. Or, you could essentially start a new catalog and import all the photos (and even if you do it right, you lose collections and virtual copies and edit sequence and pick flags and any photo books or slideshows, and probably a few other things that I can't think of right now) but please don't attempt this without asking for instructions. Or, my preference, is option 3 ... stop using folders for any meaningful organizing, begin assigning keywords and other metadata, and all future searching is based upon keywords and metadata, and if you really need to find a file by capture date, the Filter Bar will do that for you even if the photos is in the "wrong" folder.