Greetings cdav9899,
If we’re understanding you correctly, we’re working with a MacBook Air, Apple silicon.
That Mac will support - MacBook Air with M1 chip - Tech Specs
Thunderbolt 3 digital video output
Native DisplayPort output over USB-C
VGA, HDMI, DVI, and Thunderbolt 2 output supported using adapters (sold separately)
If the cable isn’t working and your Mac is not recognizing the external monitor you can try a USB-C to HDMI adapter - such as this one: Belkin USB-C to HDMI Adapter - Apple
Also though here are some articles with troubleshooting -
• Connect a display to your Mac
• If your external display isn't detected or appears blurry when connected to your Mac
Thanks.