For what it's worth... another possible way to skin this cat:
Have a Mac Pro 5,1 Mid 2012, Mojave 10.14.6, updated to iOS 16.0 on iPhone SE 2022 T-Mobile had this same issue AND issues sending group SMS messages that were not going through. Was receiving the group SMS with no problem though. After a lot of tinkering around including a Network Reset I had no success. However, while on an airplane's wifi I noticed that my outgoing SMS messages started going through -no problem, this is because the phone was on 'Airplane Mode.' I came back home and noticed my outgoing group SMS were fine while on my wifi with 'Airplane Mode' on. I went back to my Mac Pro, launched iTunes and had no problems connecting the iPhone while on 'Airplane Mode.' I did do force restart after setting the 'Airplane Mode' just in case. Make sure the iPhone remains on 'Airplane Mode' afterwards. This may help some people out there. However, I hope Apple picks up on this issue, this behavior is obviously showing issues at multiple levels. I always wait a while before any updates come out but this one caught me by surprise because I didn't check before doing the update. Need to be more careful next time. Good luck out there!