What do you mean by "freak out"?
Into the weeds we go...
An incandescent bulb uses a filament (normally tungsten) to create light. This filament has a fixed resistance so if you double the voltage the current would also double (V=I*R) because the resistance of the filament is constant.
6v = 2A x 3 ohm vs 12v = 4A x 3 ohm
Led's are an variable impedance load, their have a fixed voltage drop. So if you doubled the current it would half the impedance.
6v = 2A x 3 ohm vs 6v = 4A x 1.5 ohm
As a LED heats up its resistance is reduced, this allows more current to flow to the diode (because the voltage is fixed), more current causes more heat and lowers the resistance. This continues till the load going through the LED gets too high and it fails.
This is where a constant current driver circuit comes in and is what protrudes from the back of the bulb. These use a feedback loop circuit that passes the voltage through a resistor (value can be changed to adjust the current), this fixes the current provided to the LED. Depending on what part of your LED bulb circuit is failing it may can cause spikes in its current draw on the circuit. The sound you are hearing is created by the LED driver circuit switching at a high frequency. This can cause interference (EMI) that can wreak havoc with other components like the DC DC converter.
DC DC (Buck) converters use a PWM signal to adjust their duty cycle, this duty cycle is adjusted based on the circuit load requirements. This adjustment is based on a feedback loop that uses voltage as a reference. Your failing LED driver may be causing current fluctuations faster than the DC DC circuit can adjust for this might cause some sort of fail safe. The circuit also uses an inductor (coil of wire) to smooth the output voltage waveform. Inductors create a magnetic field that can be impacted by EMI.
These videos probably do a better job explaining how each circuit functions.
https://www.youtube.com/watch?v=iuMngik0GR8