According to MacTracker, an 11" or 13" MacBook Air would have originally shipped with some version of Yosemite or El Capitan, but can run anything up to Monterey.
What version of macOS did you have installed on your MacBook Air when the original SSD was working? I ask for a couple of reasons:
#1:
If you did not have High Sierra (or later) installed before installing the third-party SSD, your MacBook Air may not have the firmware that it needs to recognize the third-party SSD. As I understand it, this is the reason behind the note on OWC's site to "Upgrade to macOS 10.13 or higher before Aura Pro X2 SSD install."
https://eshop.macsales.com/shop/ssd/owc/macbook-air/2013-2014-2015
#2:
If you did not have Monterey installed on some drive, while the internal SSD was an Apple SSD, you may never get the chance to upgrade to Monterey. The Monterey installer reportedly tries to install a firmware upgrade. If a Mac does not already have the firmware installed, AND the internal drive is NOT an Apple one, the firmware installation and the OS installation fail. So you shouldn't install a non-Apple internal SSD until you have first installed Monterey on some drive on the computer. (That is, if you care about running Monterey.)