I think you are into something… I have trackpad, keyboard, headphones, Handoff-Continuity (which are supposed to rely in part on Bluetooth) and some other devices.
When I turn on an Xbox controller (I’m in game development) often the keyboard starts misbehaving badly, keystrokes can be triggered in disorder, typed letters could appear seconds letter (massive lag), etc… as if the Bluetooth controller somehow hijacked a big chunk of the bandwidth. I end up connecting the keyboard via lightning sadly.
However, one way I can consistently make it stutter is when I execute code compilation which ramps up the CPU instantly, fans can kick in seconds later, temperature heats up… this can trigger the pause of audio playback (instead of stuttering) lately. Pause as in, music that was on a YouTube safari tab stops playing, I have to go there by hand and hit they play button again. I have no clue what’s actually going on.
Other times it just stutters to muteness. What a weird bug… it does sound Bluetooth interference though.