ipad air gen 4 not support Bluetooth headphones are not supported

Have you tried a hard reset all of your iOS devices after updating them all to iOS/iPadOS 14.3.

Sony has an app for iOS/iPad OS

Maybe you need to start by actually using the app on all of your iOS devices

Sony Headphones Connect.

Tap, download/install and use.

https://apps.apple.com/us/app/sony-headphones-connect/id1168502924

I am running the latest iPadOS 14.2 on much older iPad Pro models and my wireless, Bluetooth earbuds work just fine.

Have you simply tried hard resetting your iPad Air?

1. Press and release the volume UP button.

2. Then immediately press and release the volume DOWN button.

3. Then, press and hold the Power button at the top.

You will see the Slide to Power off button, but keep on holding down the Power button until you see the Apple logo, then let it go.

Once you have performed all the steps, wait for a few seconds and your iPad Pro will boot up completely to the iPad Pro’s Lock screen.

Good Luck!

Contact Sony support.

Samsung's Galaxy witless earpods for Android devices work with iOS devices when using a special Galaxy earpods app.

Maybe your Sony earpods needs some sort of similar app found in the iOS App Store.

Not sure.

headsets needs to be put in pairing mode first time they connect to a device

read

WH-XB900N | Help Guide | Pairing and connecting with other Bluetooth devices (sony.net)