Hjgrove :
Depending on your country they have a "Data recovery" centre, that take the disk out of the hard drive and then place it onto a machine that reads that data and transfers it to another drive.
But this can be expensive so its your choice really.
Lol. No there is no such thing as a platter(disk) reading machine. That's not how data recovery labs recover data.
Even swapping the platters to another drive is extremely complicated and %99 of data recovery labs don't even attempt it.
What they would do is repair the connector and if it can't be repaired, they would replace the circuit board after re-soldering the EEPROM/NVRAM with the adaptives to the new board.
You can find companies that source these parts that will do this as well for you and it's typically cheaper than a data recovery lab will do it. Of course, there's no guarantee, but you can easily get a replacement board.