My mother’s laptop has been running as fast as a turtle on a snail going uphill for a long time now. Everything has been done to it, including formatting it and installing another, less cumbersome OS, but nothing improves. I have an HHD available, I have done some tests and it does work.
Would changing the hard drive do any good?
You can check the data the drive itself keeps about disk errors. This data is called SMART.
https://www.howtogeek.com/134735/check-ssd-or-hdd-health-with-smart/
Figure out if the drive is having problems or not, then look at replacing it.
Another thing that slows down old laptops is thermal throttling. Once again there are plenty of programs you can download to check component temperatures. Have you cleaned dust out of the inside of the laptop and re-done the thermal paste?