I’ve re-opened the 2018 feature request on this topic (originally titled “Only store password history when a new password is selected or copied”), merged the recent thread (“Generated passwords / passphrases: only list and store copied / “used” one’s in the generator history”), and modified the thread title to encompass the two key implementation suggestions — either discarding or hiding unused passwords (new title: “Generator history should omit/hide generated passwords that were never used (copied, saved, etc.)”).
The OP originally also suggested saving URLs in the generator history, but as each feature request topic should be limited to a single proposal, any discussion or voting on the URL suggestion should be relocated to the separate feature request topic “Save URL in password generation history”.