How can a constant secondary side current cause a primary current to flow in a transformer?
A picture save words.


Here a rectifed +-100Vp sine 50Hz drives a full bridge to 1H 1:10 step-up

Then changed input L from 1H to 1mH.  Notice that the rate of change of Idc and Iac increases 1000 x and never stops ( simulating saturation simulated by L rapid drop )

See the coil current rise with DC steps ( shaped by sine ). This is what I meant by staircase rise in current. Meanwhile AC current increases as well. Then diode drop increases slightly.