Recovering accidentally formatted external drive

That's a valid point. I was at my computer and had three SD cards that were full (and backed up 2X) and I just did it. When I put one of  the formatted cards back in the camara it did it's own formatting. 
The whole affair is most unfortunate...kind of a comedy of errors that will cost me a lot of time and $200. Oh well. 
I picked up a new 5TB drive today at Costco. Ordered online and was available for pick up. 
Clive

edit:  messed up the quote......but meant to include the part that referred to formatting between cameras.

I would be interested in other input about this. I had always thought I couldn't use an SD card from one camera in another as well. However, someone told me that as long as they were formatted in the camera you were going to use that was acceptable. Since I have recently moved from a Canon to a Sony I have many SD cards that were originally bought for the Canon but am now using in the Sony......so far without a problem. I have to admit that I had never even heard of formatting your card via the computer as Bruce pointed out.

Generally I reformat my SD cards (only in the camera) when they reach ~ 75% full. I also don't delete images from the card but rather reformat.

Just a follow up and confirmation of my previous statement, I looked in my Nikon manual, and their comments:

Memory Cards

Memory cards may be hot after use. Observe due caution when removing memory cards from the camera.

Do not remove memory cards from the camera, turn the camera off, or remove or disconnect the power source during formatting or while data are being recorded, deleted, or copied to a computer. Failure to observe these precautions could result in loss of data or in damage to the camera or card.

Do not touch the card terminals with your fingers or metal objects.

Do not bend, drop, or subject to strong physical shocks.

Do not apply force to the card casing. Failure to observe this precaution could damage the card.
Do not expose to water, heat, high levels of humidity, or direct sunlight.

Do not format memory cards in a computer.

A sad story, indeed. Of corse, eye rarlie maik erez. Although much too late for you, I have had great experiences with DiskWarrior, at least until Apple switched to APFS.

Clive, your episode reminds me of a time that we worked for hours rounding up some very wild cattle and drove them up the chute and into a 48' American Bullnose; all of a sudden, they started going in real easy --- too easy --- someone had left the side door on the sow-belly open and they were all escaping right back into the wilderness, in much the same manner as your lost computer files; our only recourse was to start back at the beginning.

I would buy a second drive of the same or larger size and "synchronize" them; thus, you would have two identical back-ups; instead of buying another drive, this would be a good job for the old drive that you inadvertently wiped.
I use the free program, Synchredible, for keeping my many drives duplicated.
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As for formatting memory cards, to avoid corrupted image files, whichever card you stick in a camera must be formatted in that (or an identical) camera.

It matters not whether a card has been used in a dozen different brands of camera, so long as you format it in the camera it will be used in.

Formatting memory cards in a computer DOES NOT format them for use in a camera.

We have seven different models of Canon camera and each model uses a different naming and foldering system; you can use a card formatted with the exact same make/model in an identical camera, but not same make/different model, as that different model may use a different layout.

Once a particular card is formatted in a camera, so long as it is only ever used in that camera, there is no need nor benefit of formatting anymore; any erasing of image files can be done when the card is in the card reader, so long as you DO NOT format in the computer and that card will remain associated with the camera with no need to be formatted in the camera again, UNLESS the card gets used in a different camera.

Once a card is formatted for a particular camera, there are real reasons to not format again; one being, I make both a text file and a jpeg with text and put them in the "root" folder of the formatted card; I also make an identical jpeg numbered IMG_0001 and put it in the first image folder in the card.
I make the text file's name "This Camera Belongs To" so anyone seeing it will know to open it to see the information.
The reason I number this jpeg IMG_0001 (or whatever numbering convention the camera uses) is so that it will always be the very first image anyone will see if they look at it on either the camera's screen or on a computer.
On both, the text file and the two jpegs, are all possible means of contacting myself and my wife and something to the effect of Please Return To etc., etc. or better yet, This Camera Stolen From etc., etc.
I never remove these files from the memory card.
If I were to format the card, these files would be lost and I would have to put the card back in the reader and load the files all over again; I might forget to do this the one time that it counted.

I know there are many that will argue the point, but I will say it again, once a memory card is formatted for a particular camera and only ever used in that camera, there is absolutely no reason to format it again.
Look at it this way, when you put a new drive in a computer, before it can be used in that computer, it must be initialized and formatted; once formatted, that drive can stay in there until the bearings fly out and never ever be formatted again; your camera works on the same principle.