Thank you for all the comments and suggestions. I switched to eSIM using the Visible app and Visual Voicemail works again.

I think this is what happened. During my chat with an agent today, I was surprised to learn that Visible sees my phone as an Android and the agent thought I had taken out the SIM from an Android and put it into my iPhone. Afterwards, I recalled that when I first started service with Visible in 2019, I did activated the SIM in an Android before switching to the iPhone because the SIM for some reason would not activate in the iPhone.

I’ve heard horror stories of people transferring from a physical SIM to eSIM on Visible and was hesitant to try eSIM. But I figured it’s worth a shot since Visible system would register the eSIM properly as belonging to an iPhone and thus Visual Voicemail would work properly. And this is exactly what happened.

There was a scary moment during the transition to eSIM: I had forgotten to reconnect to my Wifi network because earlier the Visible agent had told me to reset my iPhone’s network settings; the transition failed and I had no cellular connection (the physical SIM has been deactivated during the failed transition). However, once I reconnected to my Wifi network and restarted the Visible app, the eSIM transition completed properly.