The coil is probably non-magnetic copper, so no serious concerns about storing that part of the unit. The housing might be steel, especially if it’s not a marine specific unit, but I’d be no more concerned about that than a toolbox. The cookware certainly is magnetic, so yes, be careful it’s not too close to a flux gate compass. As others have said the induction energy is probably oscillating so I doubt there’s any visible effects from that, especially at a distance.
Plus, if you have enough energy to induction cook you could just use GPS Course Over Ground instead of magnetic heading if you’re really concerned.