I’m not sure you’re going to be able to at the present time because of the following conflicting facts:
I believe at the present time that the double press for the new SmartThings button is only exposed in the new app, “smartthings ( Samsung connect)”
in order to get to the Dome siren sounds, you have to be using a custom device type handler, and at the present time custom device type handler’s mostly don’t work with the new app, you have to use those with classic.
So it just may not be possible right now.
Can you make it work with just a single press?
There is a modification you can make to some custom device Handlers that will let them be used with a new app but it doesn’t work with everything.
Use @krlaframboise version for the Zooz chime, which also works for the Dome unit. It uses switch dimmer settings to trigger the 10 chimes. So you could use any number of smart apps on the Classic or new app to trigger them. [RELEASE] Zooz Smart Chime