iPad Air 16.3 is not sending or receiving sms

If you have an iPhone - and both iPad and iPhone are signed-in to iCloud with the same AppleID - to send SMS/MMS messages (green bubbles) from your iPad you must explicitly enable Text Message Forwarding and MMS for your iPad on your iPhone...

On your iPhone:

Settings > Messages >

• Text Message Forwarding - set to ON - and explicitly enable your iPad from the list of devices.
• MMS Messaging - set to ON

Also ensure that Messages in iCloud is enabled on both your iPhone and iPad:

Settings > [Your Name / AppleID] > Messages - set to ON

Additional information can be found here:

How to forward SMS/MMS text messages from your iPhone to your iPad, iPod touch or Mac - Apple Support

Same for my ipad since the 16.3 update and none of the above suggestions were issues for me. My settings were already like that.