Good suggestion, however, it said "There was a problem connecting, try again later" and went no further. Once I turned off airplane mode, it just greyed out again when I touched it. I then switched to the Google Messages App as my default SMS App. ...
Thanks for the link, this now clearly is a bug in Samsung's Messages App. On that page it mentions: To disable Chat features and return to Text (SMS/MMS) for Samsung Messages, open the app select the three dots on the right-hand side of the screen, ...
It's the built-in Samsung Messages App going by the icon in the task switcher: I might try later switching to the Google messages App as the default SMS app.