My situation was similar to yours.
Short version: if ddrescue through the SATA port to a docking station doesn't work, you'll probably need outside help from someone who has Deepspar or Atola tools.
Long version: I had a Western Digital hard drive crash and I lost a lot of time. I used to buy one or two WDs a year but the recent ones are too electronically fragile for me, whether desktop or portable. In fairness, I also had a damaged Samsung at the same time, but when I replaced it with a WD after recovery, the WD crashed within a month. This might be from the new WD encryption hardware, which I do not need. I don't have the budget to experiment with brands and the data are too valuable, so I switched to a Seagate without encryption hardware, and it has been working fine for more than a year.
There was no mechanical damage to my drive (it wasn't dropped, probably there was a power surge during Hurricane Sandy, causing electronic damage). It appeared intermittently in the file manager (Windows Explorer), sometimes in Disk Management, usually in the Device Manager. The data were quite valuable, some of it was my wife's, and the backup was not in place due to a long trip and moving house. The experience was horrible.
How I did get all my data back? First, I tried many available Windows tools, none of them helped, and unfortunately they mostly wasted my time and energy. Then I removed the drive from the plastic enclosure, fit it into a Thermaltake docking station, and plugged it into the SATA port. I did not remove the hard drive's inner case and expose the platters, which can cause permanent damage to the data. With this setup, I used GNU ddrescue. This still didn't work. If ddrescue isn't doing the job, then it's serious. So at this point I needed outside help.
Apparently, hard drive recovery with hardware tools has become a lot cheaper in recent years due to in-house corporate and government needs, and a highly controlled clean room isn't always required. It depends on your situation. Deepspar and Atola are two big manufacturers of these tools, but there others. These tools make a bit stream image of your drive. Some computer repair shops have these tools, which can access the drive directly in a manner that software alone cannot (i.e. force the disk to spin, use recovery profiles, change firmware, etc.). Sometimes, a circuit board piece has to be replaced, but this should only be done by people who know how to do it with the right tools and boards, since a newbie mistake can be costly and irreparable.
I didn't have the money for DriveSavers, which may be perfect for severe damage, for super private data or expensive data, and for other such needs. I found a few places offering cheaper data recovery using the hardware tools I mentioned. I went with $300 Data Recovery, but if you search, there are other places with comparable services and prices, perhaps closer to you or better for you. It ended up costing more, but it worked. Defragmented data on HDDs are easier to recover. SSDs are harder to recover, but they can be saved in some cases. You can check out the forums of HDD Guru and Data Recovery Forums for more information.
No one in my circle was interested in my agony, which may be why I gave you lots of detail. I hope it benefits you.
And I'm not endorsing anyone or hating companies. I came away from the experience with all my data and deeper understanding of hardware and computing. I'm just reporting my experience and what worked for me.