“Connecting it to the destination causes the browser to actively process the graph, even though the final volume is zero.”
A sawtooth oscillator wired through an analyser into a gain node set to zero. You hear nothing and the browser processes audio the entire time you have the tab open. The side effect is that Windows keeps the Bluetooth audio path alive and your headphones stop switching back to your phone. Tracking got aggressive enough to break unrelated hardware, and it took someone debugging their headphones to find it.