iphone voicemail greeting

I am curious if anything on your voicemail works. My wife (iPhone 12 Pro) also started seeing issues with her voicemail. For her, she can not retrieve greetings, update her password , or see voicemails from the iPhone "phone" app.  If she calls into the voicemail system (hard press 1), she can listen to her saved messages, hear her greeting , and change her password. We think maybe this started with her update to iOS 16. So far, after 1 week, T-Mobile support has been unable to resolve this and at time seems to not even understand the issue. Twice we were transferred to Apple support and they confirm it is a carrier issue. She also went to the T-Mobile store, and the store manager also believes it is a carrier "back end" issue.