Here are my two cents. Bottom line - I had this issue and it’s now resolved.
I’ve been with AT&T for over 20 years. Every iPhone I’ve had, back to the original iPhone in 2007, has been with AT&T.
In addition to the recent iOS 13.1.3 release, nobody has mentioned that AT&T issued a cellular update (to version 38.1) late last week.
Anyway, I called AT&T after my visual voicemail disappeared for the first time ever a few days ago, and standard remedies like Reset Network Settings did not help. AT&T rebuilt my mailbox. It turned out I had one saved message in the old mailbox, and the technician asked if it would be OK if I lost that, and I said that was in fact OK. It turned out the message actually re-appeared in the rebuilt mailbox. When rebuilding the mailbox, a new passcode is required. My old passcode was four digits, but now AT&T requires at least seven digits! I had a previous custom greeting. That was lost and I had to re-record it (or use the default greeting).
Anyway, this all occurred about 24 hours ago, and all is still working fine.