How to put a 'line label' not 'on' a line, but just above or below it?

is it possible to put a line label just above or below the line, but not ‘on’ the line?

Note that I still want the label to ‘stick’ to the line when the line moves, so I don’t mean a separate label.

Yep! Definitely. Add text to your Canvas and then drag it on top of your line. (Or, you can select the text tool, click the line.)

Then, look for the Geometry Inspector. Change to Parallel, then pick your offset!

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BTW, I just ran into similar situation using Adjustable Arrow from built-in stencils menu. This control doesn’t seem to be available for Adjustable Arrow connection, only for plain arrows