This seems to be happening only on certain operators, which suggests that the VoLTE modem configs might be wrong for those operators, causing SMS to fail even if calling works. It’s very difficult to reproduce such problems outside of the problem network, so it would be really helpful if someone on an X10 II could see how their VoLTE is configured and see if there are any alternative configurations which might work better.
See this thread for details on where these configs can be found:
For the Xperia 10 III, the modem configs are more self-contained in the modem, and though they could still have issues, it might be much harder to fix.