I have switched to Signal and using it for messaging and noticed at random times it cannot send messages. It will prompt and state that the message could not be sent and check your connection. Thinking this was completely a Signal issue, I switched back to Messages and all seemed to be fine for a couple of weeks. Then all of sudden the same kind of issue came up!
I've tried both on wifi and off (although I don't think SMS goes over wifi?) and I have tried resetting my network settings. Factory settings the phone is something I really do not want to do but I need to be able to communicate with people.
I have a S21 Ultra and on the AT&T network. I have noticed some other posts about SMS issues but they all seem to be varying apps causing the issue but I am starting to wonder if Samsung has a bigger issue with the underlying subsystem for messaging.