I've got the same problems. My advice to anyone is do NOT update to IOS 16.1.1
I just heard from a guy standing at a gas station he bought the latest iPhone and it's been a disaster for him. He was having issues he's never seen before, calls not working, having to do multiple reboots, I felt bad for him. Didn't think to connect it to the latest IOS 16.1.1 release. I went ahead and updated. Boy am I sorry I did. Now I'm having the same issues he was having with the new iPhone.
Now with 16.1.1. when I dial out, there is a long delay (can be 10/20/30 or more seconds) and then the person on the other end is connected but they cannot hear me nor can I hear them, sometimes the sounds will engage, sometimes not. If it does not and I select to end the call, the software displays "ending call" or similar message and then hangs. I have to reboot the phone. Trouble is, I depress the two buttons on each side of the phone to reboot and there is again, the same delay. Can take 30 seconds, up to several minutes before I can get the buttons to respond. Sometimes it will finally end and release the screen with the ending call message, but then if I call back, same issue. And that release of end call screen hang takes forever. So rebooting is quicker, though also takes up to many minutes to get the phone to respond to the button depresses. This version update is a disaster. I use my phone for business and this issue is going to force me to go to another vendor if it's not fixed pronto. Since I've not been able to get Apple to fix the delay on my contact searching after spending hours on the phone, which causes all sorts of business productivity issues, now that these delays have moved into phone calling and then requiring constant resets, I don't know what to say. I hate I'll likely have to switch to a competitor.
Was on with Apple for a couple hours doing various things like resetting network settings, etc. last night, removing a VPN I don't even use, pulling out the SIM card to reset it, a variety of things for some of which I had to drop off tech support (reset phone) to try. I think they guy may have attempted to call me back, that was the intent, but I can't sit around all day troubleshooting. Anyway, I get up this morning and same issues. Nothing he tried worked, which, incidentally, I didn't think had anything to do with the problem. I called my carrier. They have no issues reported. Again, the network reset did NOT fix it.
There was a bug that popped up a few versions back that started causing searching in my contacts to take a really long time. Stayed on with Apple tech support many hours and couldn't get that one fixed. This issue never went away with subsequent releases I did a work-around, for at least for regular contacts I had texts with, going through the text app to the contact number. That improved my productivity enough to get by.
I suspect there is some sort of order of execution within the software that has gotten messed up such that it is causing the delays. But without standing over a tech walking through the code, I wouldn't be able to figure it out. I'm a systems designer, but not a coder, though I've troubleshot multiple system issues in the past and worked briefly for an ERP systems company. This definitely appears to be a system's order of priority and execution problem or some such, on the surface. The things they are trying to do to fix it I don't believe have anything to do with the issue. But... if I learn differently, I'll be glad to share. In the meantime, I'm faced with looking at moving to a competitors' platform for communications. This upgrade was a disaster. Maybe they'll get a fix before I have to make a change.