Hey, I ran into the same problem about a week ago. A fix that worked for me that’s not listed on the Apple website is to turn on airplane mode, wait about 30 seconds, then then it off. When you reopen the phone app and go to voicemail, visual voicemail should be activated again.
If this doesn’t work you may want to check your phone carrier plan to ensure visual voicemail is still enabled on your phone. I’ve noticed that some phone providers will occasionally (maybe accidentally) cancel free services such as Spam Block, VVM and Spam ID. All you need to do is call and ask for it back and they will reactivate visual voicemail for you for free. Once activated, follow the airplane mode trick if it still doesn’t work. Good luck!