Some ring models work with smartthings and some don’t, and this has been true for over a year, so I wouldn’t make any assumptions.
Part of the problem is that under the new architecture, device manufacturers are supposed to be responsible for the integrations. Under the old architecture, they could send one of their physical devices to smartthings and smartthings engineers would write the integration.
The ring integration was originally written for the old architecture, but now smartthings says it is up to ring to update the integration. There have been some rumors that ring was working on it, but nothing official that I’ve seen and no timeline.
In any case, the first rule of home automation applies: “the model number matters.“