Henning Paul DC4HP on Nostr: This only becomes tractable if we assume an ideal transformer, i.e., M12^2=L1*L2. ...

This only becomes tractable if we assume an ideal transformer, i.e., M12^2=L1*L2. Toroids are not so bad in this respect, but still an idealizing assumption.
Deriving this helped me cut the Gordian knot I had in my brain since the ham radio course. A transformer will only transform impedances within certain bounds, i.e., the load impedance has to be significantly smaller than the no-load impedance. Only then, Z is actually multiplied with L1/L2, i.e., n1^2/n2^2.