Lightroom Classic 9. Why does it make a copy of every photo? Which one is best to edit with?

It's "possible" that when you created the collection that appears to be shared that you chose the option to create the collection with virtual copies, because that is one of the options that is available. You won't be able to find those virtual copies anywhere on your computer. They are simply additions that are in the Lightroom catalog. Nothing to worry about really. That's the only thing I can think of right off hand.

All of the copies are virtual copies, and they have the Mark indicating that they have been shared at least with Lightroom.adobe.com or Lightroom for the cloud. Apparently you are displaying the images in the folder, and not in the collection that has been shared. It is difficult for me to know exactly how you are managing your images. If you go to your collection in the library and choose the collection that has those images, I suspect you will only see the virtual copies that have been created.

It doesn't matter which one you perform the edits on because Lightroom doesn't make any changes to the file itself. All changes are simply stored in the catalog. But what happened that indicates that every picture now has a copy? That isn't normal. Can you post a screenshot that illustrates the problem?