[JeremyHerrman]

Unfortunately the nearby headphone notifications are not generated by an app, so you can't use the normal notification banner settings. The only way I've found to disable them is to go to Bluetooth preferences (while the headphones are connected), click options next to the headphones, and change the "Connect to This Mac" dropdown from "Automatically" to "When Last Connected to This Mac".

I'm not satisfied with this solution since I enjoy the automatic switching between devices, but I'm driven crazy by the notifications that pop up on my mac literally as I'm listening to music with those headphones on my iPhone. C'mon Apple - this is all within your ecosystem!