Is the Square contactless card reader an accepted device for the MacBook Air 2020?

No. The contactless reader is designed to work only with mobile devices. The Square itself is app is obtained via the App Store.

The only thing that works directly with a Mac is a swipe type reader. It's available with an 1/8" or Lightning connector. When you're in your Square account via a web browser, the Swipe Card reader is a choice.

To tell the truth: no idea. Did you check with the developer to see if it is compatible?

If you go to their website, it lists as being compatible with iDevices; no mention of macOS devices.