Incoming calls go straight to voicemail without ringing or notifications

If it's random, with calls from the same number ringing sometimes and not others, then it may be an issue with your cell service despite what AT&T says. I had an issue in my previous residence where I was on the ragged edge of reception and if the cell tower was busy I often never received a call and it would, like with your phone, go straight to voicemail. This was true even though I could almost always place outgoing calls. You might look at cell strength when next this problem occurs:

https://www.weboost.com/blog/how-to-test-signal-strength-on-your-phone

Otherwise, I can only think that it is related to iPlum and you might want to contact their support resources and see if they can offer any ideas.

Regards.

If they are not showing up in the recent calls list at all, even as missed calls, then they are never making it to your phone in the first place.

Are you new to AT&T? How is the signal? Do you have WiFi calling enabled?

I have AT&T as well with poor cellular service in much of my house due to the construction. I have never had any problems however as WiFi calling takes care of it.

You may want to check in Settings and make sure it’s actually enabled. You may also want to try disabling and re-enabling WiFi calling.

As the member above said, this is a cellular service issue. Being a Verizon customer, it has happened to me numerous times and happened to others who also have Verizon.

KCBE wrote:

I have a new 16 pro and now calls sometimes (even from family) will go straight to voicemail. They never show as missed or received calls. Phone Never rings. ATT nor apple can find a reason, apple even replaced the phone and it still happens. Did not back up from old phone. The only other thing I'm now considering is that I have iplum app for a second line on my phone and question if that can interfere with getting calls. But it is so random my head is spinning.

See also here:

Why doesn’t my phone ring? - Apple Community