A Kernel Panic may indicate either a hardware or software issue while the prohibitory symbol indicates macOS is installed, but something is wrong or incompatible with this laptop.
Have you tried booting the laptop into Safe Mode?
Try booting from Internet Recovery Mode using Command + Option + R to access the online macOS installer which in theory should be macOS 10.15, 11.x, or possibly 12.x when using this key sequence depending on the exact model of your MBAir. However, sometimes this will only boot the laptop into the online macOS installer for the OS which originally shipped with the laptop which is also Ok, but will limit the options available.
If you have trouble booting into Internet Recovery Mode because of a poor Internet connection, then you can also try creating a bootable macOS USB installer if you have access to another Qualifying Mac:
How to create a bootable installer for macOS - Apple Support
If booting from external media such as Internet Recovery Mode also produce a Kernel Panic, then you most likely have a hardware issue of some sort which will need to be repaired.