Davinci Resolve - Store Clips Edited in Cut Window in a Media Folder
As of resolve 16.2, it’s not possible to organize media from the cut page that way. Switch to the edit page. All of the edits you’ve made will persist, and you’ll be able to drag timeline clips to bins from there (this creates subclips).  You can then switch back to the cut page and continue to work if that's what you prefer.