Data recovery from SSD

Have you used this SSD before with this particular Mac? If not, then keep in mind that some third party devices may not be compatible with an M1 Mac. Try testing the SSD with another computer preferably an Intel Mac or even a regular Windows/Linux PC (the physical drive/enclosure should be seen with Windows even if you cannot mount or read the data -- at least this gives you some information about the drive's health).

Also, if you are using macOS 12.x Monterey, then there is a possibility of a compatibility issue as well (more likely with the file system used on the SSD than with the hardware itself). Also a security patch for macOS 10.15, 11.x, and 12.x did cause an issue with external drives using the NTFS file system for users who were using the drive manufacturer's proprietary software to manage the drive.

Try using another cable and try connecting the SSD to another port on the Mac especially on the other side of the laptop if possible. Make sure to connect the SSD directly to the Mac since some adapters, docks, hubs may cause problems.

How long has it been since you last used the SSD? If an SSD has not been connected to power for an extended time (6+ months), then sometimes the data on the SSD can become corrupt.

As the others have mentioned you will need to determine if the SSD itself is bad or just the enclosure containing the SSD or possibly the cable between the drive & the computer. You may need to contact an independent Apple Authorized Service Provider to assist you as they are much more likely than an Apple Store to open the drive enclosure to access the actual SSD.

It really depends. If the actual SSD is dead, it's not likely coming back. Even mechanical hard drives that had head crashes that destroyed the directory tables could be scoured for information since they tended to be stored in sequential locations. SSDs tend to fail in spectacular ways where they're not as recoverable because of all sorts of things including wear leveling.

Now if the operating system is corrupted, that often looks like a drive failure. That might be possible to scour for data.

Define "dead". Maybe it is a cable problem. Maybe a port problem. If indeed the SSD itself is damaged, then no you can't retrieve the data. You can restore from your backup.