How can I evaluate which SSD adapter is functional with 2013 MacBook Air parts? I need to connect my MacBook Air 11" mid 2013 SSD drive to another Macbook since I have to initialise it in the right format.

I'm searching for an adapter that has at one side the right connector for the SSD and on the other side a USB port. 
The problem is that I don't know which one to choose since a normal SATA port would be too big.
Just to be clear the SSD I'm talking about is this one: 

it's so tiny and I don't know if there's a USB adapter for this one so I can remove the internal storage and mount it to another computer over USB or faster interface. What adapters can read Apple OEM storage from the Air?
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