SOLVED Voicemails not showing up until days after they were left

Had the same problem. Voicemails would not come through for hours or even days on my Iphone 14. No way to predict when they would come through. Definitely frustrating! 

This solution worked for me: Deleted all my voicemail messages, then deleted all the messages from the deleted messages folder, so there were no messages left. Tested, and voicemails still did not come through promptly at this point. 

Then I noticed I hadn't recorded a custom greeting since I switched to T-Mobile. I clicked to record a custom greeting, and after doing that, new voicemails started coming through in about 10-20 seconds every time. I think somehow the act of recording a custom greeting tied my phone better to their servers. To record a custom greeting from the iphone, go to the voicemail page, then click "greeting" in the upper left corner, then click the option for a custom greeting and record/save it.