Adding my own experience into the thread as I've had the same issues on my iPhone 11. Bluetooth "stuttering" or being garbled on my AirPods, Audi MMI system, Sony XM3 headphones, etc. Doesn't matter the device. Now with working at home, I've been told that the audio is garbled on my microphone while on the AirPods as well, so I've had to run meetings with speakerphone instead of using any Bluetooth connected devices. I haven't had any issues with the iPhone mic or speaker at all, just Bluetooth devices. When it first started last Fall right after I got my iPhone 11, it was much more infrequent and I thought it had something to do with someone else's Bluetooh device "interfering" with mine's signal. I mostly only used my AirPods & headphones in the office where I was in close quarters with a lot of other Bluetooth signals. Then it started in my car and began happening more & more as I used my Bluetooth devices more this Spring.
I put a ticket in with Apple earlier this Spring after I started working from home more and the stuttering made my Bluetooth devices nearly unusable. They tried to have me update to the latest iOS (I already was) and went through their typical protocol until they ultimately just sent me a replacement via AppleCare+. The problem seemed to be fixed on the new iPhone 11 at first then started to (seemingly) gradually get worse.
I have posited that it has something to do with notifications or something with Background App Refresh, as others in this chain have noted. It has seemed to be tied to when I receive notifications but has also happened when no visible notification comes in. However, since I have so many notifications turned off, I have wondered if it's actually tied to an app refreshing in the background.
I've also rarely had the issue when using my XM3's on flights. I just had a couple several hour flights and the issue maybe happened once or twice if that. Of course, while I'm flying my Wi-Fi is on but my Cellular is turned off. Could that have something to do with it?
Either way, it's super frustrating. I've thought about selling the iPhone 11 and going back to an older phone, or going with the SE to see if that fixes it. Kudos to those of you who have reset their devices to Factory Settings, I haven't been that desperate...yet!