You can either give it a go yourself - see these links for software available:

https://www.techradar.com/best/best-data-recovery-software

https://www.tomsguide.com/how-to/how-to-recover-data-from-a-hard-drive

… or search online via Google etc; for data recovery services near to where you live.

HTH

I was advised to take the drive out of the box and connect it directly to the PC via the SATA interface. Now I have the following picture.

The picture you posted is really bad. If you are lucky, ‘just’ the partition table has been destroyed, and that might be recoverable.

Good luck recovering anything from it, via the links provided previously. I hope you did not have Bitlocker enabled on this drive.

There are tools that will recover your partition table, the first step you have to do. Once you have it back you can then try for your data.

A reputable data recovery service is likely money well spent as one oopsie poking about can remove the possibility of an easy recovery.

I did manage to solve this problem.

First, I managed to make a copy of the damaged drive using Clonezilla.

I came across this video tutorial.
 

True, it cost me $97.95, but that's nothing compared to taking the disc to a technician. I risked losing my files forever. But I can't afford to pay a lot of money.
Let me tell you a little bit about how I did it.
I downloaded Hetman Partition Recovery , the program displayed my RAW drive, which used to be FAT, and started a full scan. It found most of my files and successfully recovered them. Yes, it couldn't recover all the files, but I was lucky: I recovered the most important ones .

And yes, make copies of important files (discs) for the future.

Also, thanks to everyone who tried to help me)