Fixing Bluetooth stuttering in macOS
After doing a clean install of macOS Catalina on my MacBook Pro, I noticed that, while listening to music via a pair of Bluetooth headphones, either the mouse pointer on my screen would start lagging or the audio would start stuttering every couple of minutes, and it had been driving me nuts.
I tried numerous things to remedy this like tweaking the audio quality, resetting the Bluetooth module and resetting the NVRAM - all to no avail. Eventually though, while browsing the system preferences, I noticed that 'Handoff' - a feature that lets you 'hand off' tasks between iOS, macOS and watchOS devices - was enabled and it too uses Bluetooth.
Handoff can be a great feature if you're bought into the whole Apple ecosystem, but truth be told, I can't remember really using it, at least not between my Mac and other devices, so I choose to disable it. I haven't experienced any lagging or stuttering since.
You can turn Handoff off via the General system preferences panel, which you can reach via → System Preferences → General → Uncheck 'Allow Handoff between this Mac and your iCloud devices'.