The "comes online" alert is possible if you choose to be notified when the person becomes available, but it's capped at stalking 15 people I think. Not the best but achieves that goal.
But it was damn handy sometimes. Teams doesn't have this feature.
What was more of a lifesaver was the not showing status to some people though. There was one guy who would consider me his personal support person and this was really annoying. I know it's not normally considerd a good thing to solve a human problem by technical means. But for me it works just fine and much better than taking it up with the person themselves.