I have a slightly different procedure that I did for mine. Here is what worked for me. My wife was out of town recently so her iphone 16 Pro went to satellite mode for some of the people she was messaging but not all. When she returned home her phone was still stuck in satellite mode for anything I tried to message her. Tried everything and finally found this combination worked - step by step. Make sure you have both phones in hand cause this procedure will go quicker.
1) On both phones navigate to Settings / Apps / Messages. Turn iMessage off for 1 minute. Then turn back on
2) On both phones navigate to Settings / Apps / Messages / Send & Receive. Look at the bottom of the screen - it will say Apple Account followed by an email address. Click on that and click Sign out.
3) On both phones on that same screen click on 'Use your Apple Account for iMessage'. Then click Sign In. Wait about 10 seconds and it will sign you in (or you will be prompted for your applie id and password). Go ahead and sign-in
4) With both phones in hand, delete the message thread on both phones. So on her phone I deleted the thread from her to me. Then on my phone I deleted the thread from me to her.
5) On both phones turn off WiFi (go to Settings / WiFi and turn OFF)
6) On both phones go to Settings / Focus / Share Across Devices (and turn OFF)
7) Hard reboot on both phones (press volume up, press volume down, then press and hold right side button for 10 seconds until phone reboots)
8) On both phones turn airplane mode to ON. Keep it on for 1 minute. Then turn it OFF on both phones
9) Hard reboot on BOTH phones again
10) On both phones turn WiFI back on and connect to the same WiFi network. You can change it to another WIFi network later - for now we are just refreshing settings and trying to break the satellite connection.
11) On both phones go to Settings / Focus / Share Across Devices (turn it to ON)
12) Now try sending a message - you should see the 'is only on satellite' message is gone now. If you can send the person a photo then that is additional proof they are off of satellite mode.
Hope this works and fixes it for people!