About 20 years ago my mother in law lost 3 months of invoices from her business. I had read a bit on specialized data recovery services and told her to expect something in the $2500 range and to stick with national-level specialized companies. She left it with her (generally incompetent) IT provider, but lost patience after 3 weeks. Luckily, they did not damage the data, she contacted a reputed big firm, her wallet got a lot lighter and she got her data back within a week.
Like @Michael Johnson says, shop around. Since you should avoid dealing with local IT repair shops (I love mine, I just wouldn't use them for this) you have the whole country to look at. Make sure that they've been in business for a while, do only that, and are capable of handling the real hard cases (clean room disassembly and the like). Recovering hard disks is a specialized skill, requiring specialized procedures and equipment. Either you're in that business or you're not. I can think of plenty of things that could irremediably lose the data once more aggressive procedures are taken - that's why you want the pros.
Then contact your shortlisted providers with a pre-written note on your symptoms so that each gets the exact same story. If any one of them picks up on something that makes it seem like it's less serious (like the fact that it still spins and it could be "only" a BIOS issue), they may either quote a lower price or point you back to non-specialized people. Still, unless they have a good reason for lowering their price, the 1500-2500, on success, is what I would expect.
If you're still stuck at specialized care, I'd go with the middle bid, just like is often recommended for home renovations.
Before committing to the full procedure, you could, if you have a good local IT repair shop you trust, ask them to connect to your drive from alternative machines (maybe a Linux workstation), with the express understanding that they would not do anything else than a straight simple read without your express approval.
Also, stating the obvious, check your SATA cable. Does it work on something else? If you're not 100% sure, get a new one just in case. Maybe you could also look at it from a friend's computer. If it seems like it connects better, but still doesn't read, back off and just add that to your symptom list when you contact the providers.
Yours is an HDD story. I've had at least one good SSD (Samsung 850) die on me, after less than 2 years. There was no warning, one day it didn't work, there was no recovery possible either.
Next time, with SSDs, you most likely won't even have this option. Backup, backup, backup (esp with ransomware floating around). Do it on 2 different disks at least, rotating. Time Machine has saved my bacon twice, takes zero mental effort to use, and is one of the main reasons I stick to Macs despite knowing my way around Linux and Windows perfectly well.