Is my data safe if I recycle my MacBook?

As your “inoperable” MBA presumably can’t be started …

Newer MBAs with “M” processors use full disk encryption by default so your data remains protected

Older MBAs w/ Intel processors used full disk encryption ONLY if the user had turned File Vault “on.” If File Vault was “on” all data remains protected.

HOWEVER, recycling an Intel MBA which had File Vault “off” — w/o 1st removing / destroying its HDD — WOULD incur a greater risk of potential data compromise.

Identify your MacBook Air model - Apple Support

Erase your Mac first:

Erase your Mac and reset it to factory settings - Apple Support

Your data is still locked behind the Login Password to prevent others from accessing it, but it makes more sense and also recommended by Apple to completely erase the device.

What to do before you sell, give away, trade in, or recycle your Mac - Apple Support

If it is inoperable due to one of these startup screens, then you may find a resolution here that will then allow you to erase the Mac.

If your Mac doesn't start up all the way - Apple Support