Fun topic! If I would get 1€ for everytime someone asks “What is it good for?” the system would have payed for itself already!
I also use a Zigbee button from Xiaomi (~5€) which I opened to solder wires to the button base contacts.
Then attached the wires to the dumb doorbell… so i thought.
However, common doorbells (at least in Germany) use AC power (8-12V) for some reason. So I put a 12V AC relais in the circuit to accomodate for that. The outputs of that relay are then wired to the Xiaomi button contacts and will trigger the notification.
An even cheaper solution (without any gateway and fancy RF stuff) would be to use an Amazon Dash Button instead of the Xiaomi button. Same wiring as described above. So total costs ~10€. Sometimes the Dash buttons are even available for 1-2€ so with some market timing you could get even lower than 10€.
It also yields a much cleaner look than attaching circuit boards or raspberries 
