For anyone who want to set up the notification part:
It’s a bit annoying and I don’t think it’s possible to share this so you have to do that part yourself.
- Download Pushcuts
- open it > notifications > +
- call it something like "It’s someone’s birthday"
- as the default action, select the "happy birthday" shortcut
Then
- download this shortcut
- open it and select the new notification you just set up in the Pushcut action
- open shortcuts > automation
- set up a new time based automation
- set it to 00:01 or whenever you want to get the message
- select the shortcut you just downloaded
You’ll only see the message if it’s someone’s birthday and if you tap on it, it will automatically run the shortcut and open your chat app with the prepared message filled out.