How can I tell what is triggering Bluetooth in use icon on my menubar
Now, whenever a device is trying to talk to my Mac (or vice versa, I suppose) I will see the Bluetooth icon with 3-dots through it.


That's not what it means.

The icon means that Bluetooth is enabled and at least one device is connected.

From the Apple Support Document, Using a Bluetooth mouse, keyboard or trackpad with your Mac:



If you want to see what device is connected, just open the Bluetooth drop down menu.  Whatever is in bold is what's connected.