How can I recover data from a dead SSD on a 2015 MacBook Air?

There is a distinct difference between an HDD and an SSD. They are two different animals and this difference affects whether or not data can be recovered.

A rotational magnetic platter hard disk drive (HDD) works by storing information with magnetic impulses on those spinning platters. That magnetic info is written and read back by the drive heads. The magnetic info persists after a file is "erased". Erasure typically only wipes the directory info that maps where files reside, and the file data itself is untouched until another files overwrites it. This is what makes file recovery possible from an HDD.

There are consumer level utilities and services available that can be used to recover data from an HDD.

A solid state drive (SSD) has no moving parts. File information is stored in electrically charged cells. When file info is erased, the file management firmware may reset these cells almost immediately. Between that reset, the lack of persistent data and the use of data encryption (scrambling) in the newest macOS versions, recovering any useable data from an SSD that has been erased is next to impossible.

If you erased an SSD then you won't get anything back.

If you erased an HDD, then removing that drive from your computer, installing in into an external enclosure or connecting to it with a drive adapter cable to another working Mac and then using data recovery software might successfully recover some or all of the data. Success partly depends on not doing anything else with the drive after erasing it. If you continue to use it the chance of overwriting some of that data increases.

Disk Drill by CleverFiles is one respected recovery app. You'll find others with a quick search.

If you're looking to replace the drive, check the offerings at OWC/macsales.com. They do Mac stuff well.

The only sure way to recover data from an SSD or HDD is to create a backup of that data on another drive before that data is erased or otherwise compromised or the drive fails for some reason. Apple includes the Time Machine app in macOS for that. All you have to do is add an external drive. Back up your Mac with Time Machine - Apple Support

In addition…

Ubiquitous storage encryption makes data recovery yet more difficult, even for HDDs.

Rather than erasing the whole device for instance, the data decryption key itself can be erased.

No key, no data.

And Macs with T2 and newer security automatically encrypt the internal SSD.

Which means swapping the SSD storage into another device won’t have the data decryption keys.

And as was correctly mentioned, robust backups are the only way to mark data as being valuable.

Ah, and another retitled thread…

You're welcome.

It's always fun to get new toys.