If you can get the required parts in the single quantities you'd need, you may want to consider a battery voltage suitable for the induction stove to run directly off of, so you wouldn't need the dance with a bigger inverter and that.
Just need a grid-powered charger for the battery to replace the sun with if you worry about running out of electricity to cook.
Thanks, I will keep voltage in mind. I have ample wind so my long-term plan is solar plus small windmills on the roof. For bigger cooking sessions I will have an outdoor grill, might add some burners too. This is Spain so big LPG tanks for the home are totally common.
[Edit: it's off the grid, only gets water, and I want to keep it that way in principle.]
Yeah, if it's already off-the-grid, just combine batteries with a DC microgrid if you're aiming for cheap and efficient.
If you have the charging top voltage at/below the peak of 240V mains (which is sqrt(2) higher than the rms of 240V), you can get away with using the load's voltage-adaptive power supply to handle the varying battery voltage. This will work with resistive heaters (no simple thermostats, though; "electronic trailing edge phase cut dimmer" is the technology needed, but with adapted control to work like a normal PWM), but resistive light bulbs would burn out.
There are plug standards similar to the ones used on computer power supplies that are rated as DC variants.
Feel free to stay in contact; I am looking for making use of local solar power for electronic loads that make up most of my electricity usage once I can spend the appropriate money on it, and combining it with UPS functionality as that's rather cheap to add.
I was rather talking about the required instantaneous draw which is usually too high for an average household's Solar setup.