Hello theodor_skaufel,
To answer your question, you can configure a tooltip to have a custom message shown when hovering over your label. You can configure a custom tooltip by navigating on the Perspective Property Editor for the map component by going to ui > marker > tooltip > context > text.
For the current configuration of the map component, I have tested the zoom functionality of the component and it does not keep track of how zoomed in the component is. To achieve what you are looking for you can submit a feature request at the link below.