How can I evaluate which SSD adapter is functional with 2013 MacBook Air parts?
Apple uses a proprietary connector, which is usually described as a 12+16 pin PCIe connector. Or more simply "Mac SSD".

There are USB enclosures for these blades, though they tend to be very expensive - $70 to $100. Here's one:

https://www.amazon.com/QNINE-Enclosure-MacBook-External-Adapter/dp/B076KDPZMM/

However, note that this particular one claims not to work with Apple SSDs made by Toshiba or SanDisk.

You might be best off putting it back into a Mac and formatting it and installing MacOS using Internet Recovery. (Or even buying a secondhand Apple-Samsung SSD replacement on eBay.)

Everything you need to know about Apple's SSDs in all models of Macs can be found here:

https://beetstech.com/blog/apple-proprietary-ssd-ultimate-guide-to-specs-and-upgrades