Hi there ALoafOfBread,
If a USB mouse isn't working with your Mac, you'll want to work through the suggestions in this link to see if they provide some insight: If a USB device doesn’t work with Mac - Apple Support
Keep in mind, not all cables are compatible with your MacBook Air. Have a look at this link to learn more: Use USB-C cables with your Mac - Apple Support
Also, it's likely that your adapter isn't capable of supporting a mouse:
Use the USB-A port of this adapter with flash drives, cameras, USB hubs, and other devices that connect to USB-A for data transfer or charging. It supports data-transfer speeds up to 5Gbps (USB 3.1 Gen 1).
This link provides details: About the Apple USB-C to USB Adapter - Apple Support
Take care.