For protecting the motor you do not need a fast acting gadget. The motor is not directly damaged by too much current, but too much current will lead to an eventual overheating, and it is the heat that damages the motor. And because the motor has a big thermal mass, it heats up slowly. That is why all those thermal cutouts have plenty of time to react.
For the worm gear it is differently. This may get damaged by a shockload, and even 100ms may be far to slow. If some piece of metal breaks and jams the saw, something on the electrical side will not be of any protection. Even if the power was cut of immediately, the inertia of the motor itself may be enough to cause the damage. so you need to go in another direction for the solution.
A breaking pin is a simple and cheap option.
A friction clutch may work, maybe it's possible to lower blade tension, so the blade slips in case of a fault.
And these cheap saws should never ever run unattended anyway. You should at least stay within hearing distance while it is running. For a "lights out" solution, you need a whole different set of safety precautions.