Possibly, by a lab. Definitely not DIY.
Then you probably can't afford to get the data back.
This isn't a head stuck issue where any tinkering inside alone is going to fix it. From the sound, the platters are clearly spinning up and the actuator is moving. Most likely it's failed heads and/or media damage to the platters.
You are welcome to attempt your own heads replacement if you are willing to buy a couple of carefully matched donors, but I'd say you've got about a 10% chance of swapping the heads without killing them. Also, doing this outside of a proper clean room is highly unlikely to succeed (what you probably saw on youtube was done on a much lower density drive). A 4Tb drive is EXTREMELY susceptible to problems from dust contamination.
Also, even if you do manage to successfully replace the heads, there's another 90% chance that you'd need a tool like PC-3000 (much more than a few hundred GBP) to disable some of the drives internal functions and stabilize it enough to actually read the data. Drives don't typically just work after replacement parts, not newer drives anyway.
So all in all, I'd say you have maybe a 0.01% chance of DIY recovery. Sorry to say.