This seems to come from a Turkish government paper - Sabah Daily

Here's another actual news source covering it, rather than the entertainment show the op linked to: https://uk.reuters.com/article/saudi-politics-dissident/turk...

They say that the watch was linked to a phone that he left outside (with his fiancee, who could easily have his unlock code)

I don't know the range of the apple watch - phone connection - is it bluetooth or wireless? It's feasible that wireless could have been synced at some point, perhaps when the watch was removed from the embassy.