This is incredibly frustrating but if you have no backups of the copies of the originals on the external drive, you can't get them back. The way Lightroom CC works the originals are always stored in the cloud. The local copies are just copies of that and if you delete a file in the cloud, it deletes it everywhere. Adobe also does not provide a way to get back files if you delete them from the cloud (baffling indeed!) This is why I generally recommend people use Classic instead of CC. It is a bit harder to use (but way more full featured) and doesn't sync the same way but it is much harder to lose files with it and you retain control over your files.
Some notes on Lightroom CC functionality
The Lightroom CC Ecosystem is tightly integrated across all clients. Your managed library, the original photo files, and any work you’ve done on the files are available to all clients: Desktop, Mobile and Web. When you perform any operation on one client it syncs to all the other clients. That is the nature of “your photos - everywhere”. The same holds true with deleting photos. When you delete within the Lightroom CC ecosystem, you are deleting everywhere. That is why we put up the big scary messages to let you know this and ask you to confirm.
In the Lightroom CC desktop application, there is a preferences option to “Store a copy of all originals at a specified location”. When checked it downloads a copy of all your original photo files. There is also the ability to select any album and invoke the “Store Album Locally” option. It is very important to note that these are not ‘backups’ but rather user-selected options to allow you to have access to the original files if you are going to be offline or if your internet connection is too slow to download images on-demand. When you choose to remove a file from your managed library, you are removing it from everywhere and that will also include those ‘stored locally’ images. The time it takes to sync changes from one device to another device may make it appear like this is not happening but if you allow sync to run its course you will see that when you delete it will delete from everywhere.
Having said all that, your confusion on this point is 100 percent understandable, and clearly we need to make some changes on our end.
We are reviewing the warnings we provide when you delete a photo to make certain that they are as clear as possible. We are also looking at options in the future to help customers easily recover files if they accidentally delete something they didn’t mean to delete. In the meantime, we have recovered all of the files that were deleted in this case, I believe you have already received an email on that topic. Please do reach out to us if you have any issues with the recovered files.