Iphone messages will not Synch to MacBook

Hello

Iphone 14 Messages (green app) will not synch to my new 15" MacBook M3. It's stuck at March 27, which is when I upgraded to Macbook M3 - on previous MacAir it was working well.

Previous advice leads to dead ends, because menus have changed - often offering less options.

AS things stand now:

On Macbook 'Messages' in iCloud is ON, and synced.

On Iphone in Messages settings Imessage (is switched to green) *curiously it shows it is linked to my phnone number as well as 2 emails, whereas on Macbook: Messages>settings>imessage shows 2 email adresses BUT NO phone number, and no method of entering one.

I hope you you can help. Thankyou