A routine is something GH uses to activate other devices like Homey, not the other way around. Homey cannot start anything in GH, so routines won’t be of assistance there.
Yes, you are not alone in this wish. If you search the forum you will find many more wanting it, but GH doesn’t provide the means. The only solution is to let Homey REALLY talk to GH.
Some apps allow Homey to stream to GH though, but that is then a Nest Hello question for the builders of that integration. What you ask the Eufy doorbell can do using the Homey app for Eufy.