so. what you are saying is that the cooker "can" be internally connected to just ONE of the phases? (splitting one phase to the oven, and one to the induction top?). well. that could be. i don't know. might have to open it up to have a look
but the oven part is working flawless either way. its only the induction top that is having an issue
The oven is often on/off control. The induction heaters uses some kind of dimming circuits, I don't know the specifics of this. High THD screws with the cheap zero cross triggering circuits. There is no easy fix for this.
4kW inverter will definetely cause significant current harmonics, and the source impedance defines how much voltage harmonics you will get.
It's a very common problem when people use motor drives on generators without thinking ahead. Lots of other systems sources by the generator fail to work or get damaged. Or even worse, the generator regulation fails and burns everything.
Other option is indeed that the cooker is wired incorrectly, I think that is unlikely. Easy to inspect though.