As far as I know, there is no way to use AppleScript to insert something in the menu bar, and I searched for a long time.
There are two applications that will put things in the menu bar, based on scripts of different types:
- Text bar
BitBar caused a sensation a few years ago, but it is almost dead now.
TextBar is less known, but it's a much better application, in my opinion, and the developer is very responsive. You can find examples on GitHub of the types of things you can do with.