Door bell partially rings randomly since Nest doorbell installation
While I guess it's possible that fluctuations in the Nest Hello's power usage could cause the doorbell hammer to move, I wouldn't expect it to be enough to make the doorbell actually ring.

If you add a resistor, I imagine it should be only a few ohms, but it needs to be able to handle a fair amount of power (around 25 watts, from what I've read).  It could also prevent the Nest Hello's battery from charging correctly.

Before you start messing around with resistors, try Nest's advice.  You might need a new doorbell transformer.