Issue adding messages to favorites on iPhone 16 Plus

I follow the usual steps go to contacts I select the contact I want to add then Add to favorites then I select messages it pulls up a window with the mobile number and select that number and then it goes away. I then go to messages and the contact is not there. I recently purchased an IPhone 16 plus and followed the directions to transfer. After that it showed only 3 favorites from before but I can’t get it to add a favorite to messages. All phone/call favorites Where there after the transfer.

[Re-Titled by Moderator]

Original Title: Adding messages favorites