I think I might have just killed my external hard drive

[CloudWatcher]

6. How precious is the data?

If you have the data elsewhere, then it's not worth the time & effort to get it fixed.

Otherwise, you could try and find the same model drive (new or eBay) and
swap the internal circuit board with the "new" one.

It's not something to do if you're not comfortable around computer internals, but
it's not rocket science either.

As others have said, the data on the drive's platters is probably just fine. You've
"just" fried the controller that talks with it.

Alternatively you could give the drive to a real EE and let them buzz out
the board and try and replace the fried chip(s). If you're lucky it could be
a common chip & easy enough to replace. But unless you're friends with
someone like bigclivedotcom the odds of success with this path are pretty slim.