Hi! Happening the same with iPhone 6S with iOS 12.0 (also happening with 11.4.1). With SoundPeats Q9A headphones and also with Sennheiser HD4.50BTNC...
I didn't realize about the beep since two months ago or so... But know I can hear it... it's here all the time! For me it's happening with Music App (NOT Apple Music), when a new songs start always sounds a beep. Also, at everyplace, if I push up/down the volume also there is a beep... It's really very annoying because I have other bluetooth headphones/speakers (Bose SoundLink II, Xiaomi Sports) and they are not beeping. Also, wired headphones doesn't beep.
These two headphones has noise cancelling (at least as per technical sheet) but really I don't know if it is the issue. And probably prior to 11.4 there was no beep because I didn't realize about that.
I've tried everything (go to maximum volume and after go down didn't worked), the only thing that I didn't perform is a phone reset... but I don't want to do that!!! Same headphones are working well with other devices (Android, iMac, etc.)
Seems that it is an issue with iOS as boulderskies says, hopefully it is solved quickly... but after a couple of new versions it was not solved so really I don't trust Apple to solve this... maybe the want we buy Airpods or whatever...
Thanks all for your comments.