Henning Paul DC4HP on Nostr: This is obvious when you think harder about it, using that rule of thumb from the ham ...

This is obvious when you think harder about it, using that rule of thumb from the ham radio course, an open loop, i.e., Z->\infty would have been transformed to Z->\infty on the primary side as well, but instead we see the no-load inductance, because the assumption Z << j\omegaL1 no longer holds.
That also implies that a transformer becomes "better" at transforming impedances the higher its no-load inductance is.