If you think you might be able to afford professional data recovery, and that is a path you want to try later, then I would advise doing that sooner rather than later as the chance of data recovery diminishes over time.
If you're sure you do not want to go with professional data recovery, but rather want to try do it yourself, I would strongly advice that you stop your attempts with file system repairs, mounts, etc. right away. These tend to do more harm than good. Instead the best way to proceed is to take a copy of the disk and only work on that copy - never touch the original hardware.
In order to take the copy, I would recommend using the program "ddrescue". First install Home Brew, and then run this command in the Terminal:
brew install ddrescue
The ddrescue program allows you to take a bit-for-bit copy of the drive. Compared to ordinary dd, the ddrescue program can skip unreadable sections of the drive, and it is possible to do multiple attempts at reading problematic parts of the drive.
Familiarize yourself with the documentation here:
You can find the device name of the disk in Disk Utility. For example it might be /dev/disk2. First ensure that all partitions on the drive are unmounted.
Then the ddrescue command to copy the disk could look something like this for doing maximum of 3 retries on each read:
ddrescue -d -r3 /dev/rdisk2 mydiskimage mydiskmap
Make sure that you have enough disk space on the location where you want to save the "mydiskimage" file.
Now that you have the copy of the disk, you can use various disk recovery / forensics tools to try getting your data back.
In regards to your question about the hardware needed to do professional data recovery yourself: Even though I can confirm that it is done by humans, it is not something the ordinary home user can do themselves. It requires special training as well as special hardware and environment. In theory it is of course possible to arrange for that yourself, but building your own clean room, buying microscopes, etc. is going to cost you a lot more than the professional data recovery company charges for their services.