This issue just started happening for me a few weeks ago. iPhone 11 Pro Max. I suspect it has something to do with the new Bluetooth privacy feature. I installed a new app and opened it while my earbuds were paired to the phone. The app asked me for permission to use Bluetooth, and then problem began. I tried deleting the app to no avail. I upgraded to 13.4.1 and the problem went away. However, just the other day the same thing happened again. An app requested access to Bluetooth while my headphones were paired/on and the intermittent static skipping started again. I think both times I either selected No or closed the app.
It’s definitely a bug and I think Apple should add the ability to wipe/reset all Bluetooth settings/cache/privacy requests separately from other network settings (since deleting all your saved WiFi passwords sucks if you don’t have to do it).