Steelduck, I am having same stuttering issue on all my headphone devices (but not car or BT stereo). I have a Pro Max though (and my daughter's iPhone 11 does not have issue, so opposite of yours!).
I have made following observation (other than its driving me nuts and Apple has been less than helpful):
For me, issue seems to happen mostly in my car where I have the Phone connected to Audi BT. Seems Headphone BT and Car BT are different BT protocols or something (note that headphone only shows up in BT on upper right of iPhone screen when using a headphone, but not a car or a speaker).
I noticed that (unlike the 11 and earlier iPhones), even when using headphones (but car BT on), the Audi display shows what is playing on iPhone (but actually sounds is through headphones). So somehow, the BT is still connected in some way to Car. I noticed that if I turn the car off when listening to BT on Headphones, the audio on the Headphones shuts off (even though in theory it should not since connected to Headphones).
So, i think part of the issue is the BT is confused and trying every once in a while tries to re-connect audio to the Car BT (which might be first in line in the protocol or something?). When it tries to connect (while on Headphone), it quickly stutters/chirps and loses sound, but then comes back to sound on headphone.
So, I turned off my car BT yesterday and boom, I did not get the stutter on my headphones. I must admit I once in a great while get the stutter while wearing in the house (and nothing BT trying to connect to), but very infrequent.
So maybe you can try same fix (although not a fix, just a workaround until Apple actually fixes it). See if you have any other BT device (non headphones) that are "connected" or in range to be connected and turn them off and see if that fixes the chirp as it did for me. Who knows.
As an aside, Apple had sent me a Bluetooth Profile so they could then log my BT issues and they uploaded log last week. I spoke with a Sr. Tech for at least an hour last week. Called them yesterday to report my new findings on the Car, etc., and new Sr. Tech said he saw NOTHING in my account about the issue or any call with other tech or even the BT log I sent them. So, yeah. Bad. I just hung up since why spend all this time with them when it seems to go nowhere.