True for ordinary transformers with separate primary and secondary windings.
It goes through the galvanic connection.
Depending on the variac setting, you can run hundreds of kW at 1:1 setting (limited only by the contact ratings), at 90 .. 110 % we are talking about 10 % of the nominal power goes through the core, the rest goes through the galvanic connection.
At 5 %, most goes through the core. possibly 1/20 of the nominal power can be transferred through the iron core.