I just got off the phone with Verizon support who told me there are no notifications to tell me my voicemail box is almost full (or even full). During this time with so many robo calls, I find it hard to believe that this feature doesn't exist. It seems to me there was a feature many years ago but not anymore?
I guess the only solution is to remind myself each week to delete my voice messages. This solution sounds completely idiotic. My guess that other phone carriers offer this option.