New iPad Air iOS 15.6 - sms

iPads cannot on their own send SMS messages. They require a paired iPhone for that.

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

Nope.

iPads have never had the ability to send SMS (green) on their own. They have always required a paired iPhone to do so. They can send iMessages (blue) to other Apple devices without a paired iPhone however.

Make sure you have your iPad turned on in Settings->Messages->Text Message Forwarding on your iPhone.

Link-> What is the difference between iMessage and SMS/MMS? - Apple Support

It should be between Show Contact Photos, and Send Read Receipts. It does not appear to be there on your screen shots.

From the link above:

* Don't see the Text Message Forwarding setting on your iPhone? Go to Settings > Messages, turn off iMessage, turn it back on, tap Send & Receive, tap Use Your Apple ID for iMessage, then sign in with the same Apple ID used on your other devices.