Is copper loss present in the winding of an autotransformer?

The working principle of a transformer is that its core is energy-intensive to magnetise, so the windings “aim” for causing a net zero magnetisation. An autotransformer has a common winding section and a smaller winding section only used on a single side. The magnetisation by the smaller winding section needs to offset that by the common winding section, consequently it will carry a proportionally larger current. A proper transformer would have the common section twice, and mostly cancelling magnetisations are present in both the common sections. That causes significantly larger losses than if the currents can cancel before even turning into magnetisation.

But there is a noncommon winding section, and its magnetisation needs to cancel with the magnetisation from the common winding section. That still means significant current flowing.