Doc has reference to how to display a notification alert but not sure if there is an option to display a message in status bar that can be updated like a price ticker.
There is not a way to use AppleScript to put something in the menu bar, as far as I can tell, and I looked for a long time.
There are two apps that will put stuff into the menu bar, based on scripts of various kinds:
BitBar made a big splash a few years ago, but it's pretty much dead now.
TextBar is less well-known, but it's a much better app, in my opinion, and the developer is very responsive. You can find examples on GitHub of the types of things you can do with it.
Macs don't have a status bar; if you mean the menu bar, then no, definitely not. But as you mentioned, it is pretty trivial to use notifications with Scripting Bridge:
osascript -e 'display notification "All questions have been answered." with title "Alert: Question Answered" subtitle "Notifications could be like a stockticker?" sound name "Ding"'?