Hard drive failure: How can I recover my data?

I am currently facing an issue with my hard drive. I am unable to access it or retrieve any of the data stored on it. I have already run some diagnostics to confirm the hardware itself isn't damaged, and there are no bad sectors present. However, whenever I attempt to open the drive, Windows prompts me to format it first. I haven't dared to proceed with the formatting because I don't want to risk losing everything I have saved. Does anyone know of a specific tool that can fix the drive without actually wiping the data? If such a solution exists, could you please provide its name? Regarding data recovery software that attempts to pull files back after a format, I would prefer to avoid that route; while those programs sometimes work, I've found that many of the recovered files end up being corrupted or completely unusable.

If you’re certain there isn't physical damage to the drive, I would suggest running a full virus and malware scan first.
Download a diagnostic tool directly from the manufacturer's website to check its health. Alternatively, you could try plugging the drive into a different PC to see if the issue follows the hardware or stays with the system.
You might also consider attempting a system restore...

That is my initial assessment... though I am sure others here will have additional ideas.

Maybe try downloading a Windows Mint live USB and see if you can use it to rescue your data.

Hit Start > Run > type in diskmgmt.msc
Once that Disk Management window pops up, just find that specific hard drive in the list, right-click it, and go ahead and select Change Drive Letter and Paths...

Just swap the current letter (hit change) to something else that isn't already being used by another drive, and then you should finally be able to see all your files sitting there where they belong.