Maybe you could record your door bell as a custom wake word, and your phone ringing as another custom wake word, and so on. Then Rhasspy hopefully detects the right noise and you can react to all of these “wake words” with a script.
I don’t see anything that makes it impossible theoretically, but you’ll have to experiment a bit, and I don’t know whether it will work in practice. Most wake word engines will probably not be tuned to door bell noises but to human voices
I think you will get a lot of false positive events if you try to train a noise as a wake word. Main goal of speech recognition is to eliminate noises from speech. That’s the opposite of what you want.
For doorbells it’s easier to do this in hardware. For example use an esp8266 on your bell to publish this event. There are many examples in the web. It’s easy and cheap.
If you use Hassio, then you can use esphome to publish this directly in your environment only via configuration. There is no programming skill needed