Not all induction cooktops are created equal. European models have power factor correcting power supplies, U.S. models generally do not.
Since U.S. residential grid usage has no regulations on power factor, many manufacturers cut costs by just using simple rectifier-filter cap to convert incoming single phase AC to DC to run induction drive inverter circuitry. For residential usage, U.S. grid charges are based on true power so there is no incentive to have good power factor appliances.
Same goes for variable compressor speed inverter-refrig's. My expensive variable speed compressor Samsung 28 cu-ft has very crappy power factor of 0.6. The European Samsung model does have PF correction.
Running poor PF loads on inverters degrades inverter efficiency so consumes more battery power. The lower the PF of load, the higher the peak inverter current. Inverter losses are proportional to current through MOSFET switches and transformer.
Since U.S. market for mini-split inverter-air conditioners is small, and Europe/other countries that do use most of mini-splits built have PF regulations, most of the mini-splits even in U.S., do have PF correcting power supplies.
The power factor aspect depends on the grid supplier. In CA, the original meters did not measure PF, but with the smart meters they do and we are charged more for it even in a residence.
Some inverters are better at dealing with this PF aspect - some really struggle.