My Smart Cover does not turn on/off my iPad

I think you purchased the wrong smart cover

The magnets inside of the 2019 iPad Air 3 maybe in a different location than they were in the 2017, 10.5 inch screen iPad Pro.

You need these Apple smart covers, instead.

https://www.apple.com/shop/product/MX4V2ZM/A/smart-cover-for-ipad-7th-generation-and-ipad-air-3rd-generation-alaskan-blue?fnode=9a&fs=f%3Dcaseios-ipadair2019%26fh%3D4583%252B45d1%252B4b33

https://www.apple.com/shop/product/MPU92ZM/A/leather-smart-cover-for-ipad-7th-generation-and-ipad-air-3rd-generation-saddle-brown?fnode=9a

Other accessories cases/covers from Apple’s Website for the 2019 iPad Air 3 here.

https://www.apple.com/shop/ipad/ipad-accessories/cases-protection?page=1#!&f=caseios-ipadair2019&fh=4583%2B45d1%2B4b33

Have you tried a simple hard reset of your iPad by holding down both the Home and sleep/wake buttons simultaneously until your iPad goes to black and restarts with Apple logo, then release the buttons?

In Settings app under Display & Brightness, make sure Lock/Unlock is set/toggled to the ON position.

Just to be clear, this doesn’t turn the device off and on, it wakes it up and puts it to sleep. That’s what it is supposed to do.

Was that smart cover you purchased specifically for the 2019 iPad Air 3?

You need the Apple smart covers that state for 2019 7th gen iPad and iPad Air 3!

Bring your iPad Air 3 and test these smart covers in the store before you leave!

Best of Luck to You!