It is possible by doing the following:
The Strix Unity SDK has an event to notify when a room owner changes. The event is available as StrixNetwork.instance.roomSession.roomClient.RoomOwnerChanged. Its event handler is suitable for the processing in question.
Instead of using the event handler, if you would like to check whether the owner has changed in the middle of an Update or a coroutine, you can do so by keeping the UID of the previous room owner and comparing it with the current room owner’s. Use StrixNetwork.instance.room.GetOwnerUid() to get the UID that represents the current room owner, and compare it to the UID of the previous room owner. Note that the UID is an interface, so you should not use the == operator and should instead use the Equals method as in StrixNetwork.instance.room.GetOwnerUid().Equals(previousRoomOwnerUid).