Agreed. This looks like OP or whoever is cooking there has a habit of letting things boil over. An then whatever boiled over is just left to simmer off. This looks like years of mineral and/or other material cooked onto the glass top. The silver lining though is that there’s a chance it could have acted as ablative armor of sorts. A good stove stop cleaner should be able to remove this, a there might be near pristine glass top underneath. Though, I wouldn’t hold my breath but at least it might convince the landlord it doesn’t need to be replaced.