I purchased a MacBook Air and did not receive free apple tv+

See if the "Redeem your free year of Apple TV+ now" section of the following will work for you: https://offers.appletvapp.apple/

You need to redeem the offer yourself and do so within 90 days of activating the new device

Open the Apple TV app. Make sure your device is running the latest version of iOS, iPadOS, tvOS, or macOS.

The offer should be presented immediately after launching the app. If not, go to the Apple TV+ channel page where you’ll see the offer.

Tap Enjoy 1 Year Free.

Apple TV + Offer

https://support.apple.com/en-us/HT210573