I had this issue right away, let's say minutes after setting up my new iPhone 12 (transferred from an XR) on the AT&T network. I tried the ol' resetting network, restoring from backup, etc... Nothing worked, 48hrs later I had enough, I called AT&T and granularly got to an engineer. Did a bunch of tests with my iPhone 12, from my SO's iPhone 11, and a spare Android (work) phone. That night they were able to fix incoming calls from non-AT&T & non-iPhones and also they had to RESET my 5G config "profile" cause I noticed it kept turning on/off randomly, but alas texts from an Android were still on hiatus. Needless to say, they escalated a ticket by the end of the call which I received a copy of that "internal" ticket. Come Monday around 2am or so my iPhone started going bonkers (buzzing) non-stop. With one eye semi-open, I noticed all the missing non iMessages started to flow-in, about 60 or so I missed on/off since that Friday, plus missed phone calls outside of AT&T network and a few voicemails as well.
So the best advice I can offer is make that call to your wireless provider and get an engineer team involved.
SIDE NOTE: My iPhone 12 was purchased via the Apple store instead of going through my normal AT&T trade-in (the first time I've gone this route). So I don't know if that made a difference with the small inconvenince in my experienece.
Cheers!