What about making your own automatic extinguisher activated only at night or when there is nobody at home, using a CO² extinguisher directed to the server with lever actuated by a weight and an electronic control ?
Doing that a small CO2 cylinder will be not effective, you would want a large pressure cylinder with a high pressure control valve on it, and then steel pipes leading to a set of discharge nozzles so that when the smoke or fire alarm trips there is, after a 30 second delay, to warn with a siren that discharge is to occur, and allow a stop if the room is attended, to discharge the cylinder and flood the room to displace all the air in it. Replacing agent can be CO2 or even dry nitrogen, as you just have to drop oxygen concentration below around 10% to stop most fires from burning. Doing so is what the most common automatic data centres use for fire protection, using big cylinders of high pressure gas, nitrogen, Co2, Argon or other inert gas mixes for the quench gas. Some will even have a SF6 fill, guaranteed to put out even burning magnesium fires quickly and safely. Only thing it will not put out is oxygen fluoride fires, but if you have that stuff around your best bet in all cases is a good pair of running shoes, permanently on your feet.
All this for a single home server in a half-height rack?
It is not full of nitrocellulose, only electronic stuff that does not catch fire that easy...
You must suffer from fire phobia, paranoia or a real sense of humor ... You are kidding for sure, it can only be a joke ...
A simple mobile cart with a 5Kg CO² fire extinguisher placed in front of the server, with diffuser directed towards the front of the server and preconized automatic control, and it is solved.
There is no danger of emptying the fire extinguisher in the room that is not usually occupied .... At most it is necessary to provide a small delay of 15 seconds sufficient to confirm the signal of the smoke detector.
As I said, the automatic control is only connected at night and when there is no one in the house.
In the event of a false alarm, one loses a 5 kg refilling of co², it does not cost a fortune.
In case of actuating of the fire extinguisher, it should also been recomended to power off the whole server rack.