SSD Dead - "Not Initialised" - Data Recovery?

Don't intialize the disk.

Have a look with a 3rd party partition manager

e.g. Aomei partition assistant Standard edition

AOMEI Partition Assistant: Partition Software & Disk Manager for PC, Laptop and Server

Does it show the drive as unallocated space, or not at all?

You could try System rescue cd, or parted magic, maybe Linux will see the drive. If so, you can try test disk for data recovery.

If the controller on the SSD has died, then there is likely no hope of rescuing the data. It would require a controller replacement, which most of us mere mortals cannot do, as it requires very specialized equipment.

If the data is very important, you could try sending the drive into the manufacturer for repair, but they will likely reinitialize the drive wiping your data. The other possibility is a data recovery service, but be prepared for a hefty bill if you do that.

Sadly, when SSDs die, any data on them will usually, if not always, be irrecoverably lost. This isn't a put down of SSDs, it's just the nature of the beasts (more on this in a moment). I wish I could give you better news.

This is too late to help you now but, if you are able to get the failed one working again (unlikely but possible) or you replace the SSD with a new one, you need to start backing up your data on a regular basis. Any drive, no matter the quality, can fail at any time without warning with no hope of recovery. The only way to ensure the safety of your data is to have it in at least three different places, typically your computer, an onsite backup drive, and an offsite backup drive. Onsite backups can be stored in a drawer or shelf away from the computer, Offsite drives can be stored in a locked drawer or locker at work or school, at a trusted friend's, neighbor's, or relative's home, or in a safe deposit box at a financial institution. If budget constraints won't allow two backup drives (we've all been there), even one backup drive will be much better than nothing until you can afford the second drive.

Backup drives must be kept disconnected from the computer except when updating a backup. I also recommend keeping the OS, programs, and games segregated from data to make backups more efficient and faster. This can be done with separate drives or separate partitions. For the System (OS, programs, and games), imaging is the best way to back those up. an image is essentially a snapshot of your system and, like a photo negative, can be used to restore the drive in the state it was in when you made the image. I, and many others here, recommend Macrium Reflect Free.

While imaging is required for backing up and restoring the System. It's too inefficient and much too slow for backing up data. For that, I recommend using a folder/file syncing program, such as FreeFileSync. When set to mirror, they work by comparing the data drive (or partition) to the backup drive, then copy in new or changed files on the data drive that aren't on the backup drive. Any files on the backup drive that aren't on the data drive get deleted from the backup drive. When finished, the backup drive will essentially be a clone of the data drive. FreeFileSync has a feature called versioning that can be used to send the deleted files to a versioning folder or drive. This helps to protect from loss due to accidental deletion, etc. I strongly recommend using Versioning.