It sounds like you are into the realm of big boy recovery. There is no "I don't care if it takes 60 hours of my time/leaving a computer on for 2 weeks" or "I'll do it manually/code it myself" option really like there is for other things. Hardcore tools and hardcore skills is the next step, and even then it is not guaranteed.
If you are not willing to pay for someone to do the service then tooling up is probably as costly, if not vastly more so, as one shot of the recovery services. They are also not the sorts of things you can sell on that easily or turn into a business (if I am telling you all this you have a long way to go before I would consider setting myself up here -- come back when you can tell me at length what SaaS, RAID, what MTBF actually means in the real world, SAN and the main server level file systems might be, not necessarily to full bore storage bod level but enough to have a chat with one) to recoup things.
Generally such things run
1) Boot in a standalone case or motherboard in Windows and Linux (depending upon the drive and factors I have had each work where the other failed) to see what can be grabbed with standard OS file managers, disk scanners and with tools like photorec/testdisk
https://www.cgsecurity.org/wiki/Main_Page recuva and the like. If you want real fun you can also get into sector level reading and file reconstructions (hopefully your drive was not too fragmented, or RAID 0)
2) Boot one of the recovery tools the vendors offer, and are often included in tools like UBCD, hirens and whatever else.
2a) Maybe consider something like spinrite. It could work, instances of that are few and far between but it could.
3) (may happen sooner) Check the board for obvious signs of bad components and connections. Repair as necessary. You are unlikely to have schematics for this one either so I hope you are good with electronics, might be able to source a matching working drive
4) A basic USB caddy will do 95% of the work but there are specialist ones that will skip over unreadable sectors, approach from the back of sectors rather than reading raw files, handle corrupt file allocation tables, do repeated reads and other stuff that bumps the rate up a bit more than either a caddy or motherboard or hard drive card with stock commands only available.
5) It is often the grease in bearings that goes so some combo of heat, cool (see drive freezing, remember to chuck a silica gel packet in there to soak up the condensation) can do the trick, and you might be able to tickle the motor with a slightly higher voltage (possibly having isolated it from the board so as to not backfeed the PCB and blow that up, and if you can't tell or would not know to look for some kind of resistance testing in that then... you have even more learning to do). I don't know that I have heard of a stuck head in many years that a little love tap sorted (and if you do it you might actually screw up the head as the little bond wires are not the strongest things around) but there is that too.
6) I have had drives have so many bad sectors that they overwrite the good parts of the firmware and die accordingly. This can be somewhat solved with a board swap (though while technically easy that is not a path without its own perils) or reflash, though there is no standard method of reflashing so hope you are up for building a JTAG connector or i2c setup or one a thousand other such communications protocols and possibly figuring out what a vendor has for this sort of thing.
7) Now we are in the really big leagues (though buy in for a recovery level dock is usually several hundred). Here the combs, clean room cabinets and knowledge of what to do (again don't misalign the platters) are the order of the day. Oh and be prepared for much of this to become useless as we increasingly shift to SSD over the coming years (indeed it is already happening), SSDs have upsides and downsides here.
You will also be faced with having to source a suitable donor drive. It might well come down to having to find one of the same batch. Quite possible for some types of servers and workstations but if you have a meh model from a fly by night brand (which is a lot of consumer computers) that has not been sold in 10 years and barely sold anything before then you are potentially in for a nice uphill struggle. Drive recovery firms will also take note of the most popular drives in general and in laptops and vendor machines and often have them in a library or contacts enough to find such a thing (also if they charge regardless they don't care if they ultimately fail).
Oh and while the risk is usually small 1) through 6) can also make the lives of someone doing 7 that much harder, or necessitate going right to 7 where one of the other levels might have worked. While very much in the "more art than science" side of things (drive recovery in general already has this in spades) there are things you can look at and questions you can ask that would get you to skip one or more of those.
As was mentioned if you opened the drive up then you might be at 7, or indeed a super advanced version of it (couple of goes in an ultrasonic, which will want to be in your cleanroom as well, might not do this one), by virtue of that alone.
8) Usually reserved for massive international companies, universities, super specialist firms and intelligence (think NSA) level government players. Here you can try to play with things like scanning electron microscopes to recover a few kilobytes a day -- great if you have recovered a toasted drive from a hut somewhere and that few pixels of photo or lines from a document (that the bad guy somehow did not encrypt) is enough to send in the boys or win a court case worth billions, if you just want to recover your treasured holiday snaps then eh (even if said snaps contain people no longer in your life that you would like to have pictures of).
In my general day to day then 1, 2, 3 and 5 are the only things I generally offer to people, anything beyond that and "it is dead, mate. This is why we have backups" and then we get to figure out if something is still on another drive, got emailed around, online somewhere, able to be remade from whatever I can recover, able to be scanned in, able to be restored from paper records...
If it is going to be a real pain ("lost my accounts, now I will be fined out of existence" being about the level) then I might offer higher if a search of all the usual suspects and my list of computer vendors yields a decent possibility of a donor drive.
