Wait a minute. If the two line side connections are still made, there will be magnetizing current.
Tom
See prior post and "measure it with your clamp Ammeter".
Some autotransformers MAY have their one and only coil across the line. See also "variac".
Others do not.
WHEN they do not, the circuit is only completed when the LOAD is connected. ergo no significant current flows (there is ALWAYS leakage of SOME kind ...if you have gear good enough to measure such..).
WHEN you have a coil
always across the line, it might be less contentious to consider it an
autotransformer arranged special case of an isolation transformer.
What would have been a fully-isolated secondary has been wired in series, out-of-phase so as to buck - or in-phase so as to boost - the line Voltage presented to the primary.
Look at the maker's schematics for the "raw" device(s). Then at the several ways of connecting them, depending on tasking.
MOST commercially-offered "buck/boost" ship with distinct and separate primary and secondary windings. They are also suited for
full-isolation use for lower-voltage loads.
These include "grounds lighting", and at anywhere from 6 to 48 Volts, quite commonly 12/24 or 16/32, much less often 24/48 or 6/12.
The PHYSICS are precise enough.
Pesky humans want lots of choices, get them, then don't all make the SAME choices when they arrange the taps for their specific application.
I try, and try HARD - so far with 100% success EXCEPT FOR my several Variacs and one multi-tapped bench test equivalent - to not use Autotransformers AT ALL.
Nought to do with efficiency, mass, space, nor even value-for-money.
I simply have a residence full of fussy electronics gear adjacent a shop full of NASTY, NOISY electrical gear.
Drive isolation transformers help.. would you believe "isolate"... that trash. Rather well, too for the actual environment I have to deal with. SCR-class DC drives yes, VFD's no longer.
Other than kitchen and laundry, anyway.
THOSE "inverter Drive" AKA VFD buggers are on their own. The makers have FAR better labs, test facilities, motivated staff, and deeper pockets with more MONEY in them than I do. They do rather well even when the products are mass-produced to slender margins. (LG, Panasonic, Whirlpool, GE, etc..)