Geese need more feed than ducks, and they have higher nutritional requirements than chickens, which is why they need a feed that is formulated for waterfowl or a mixed flock, typically called an all flock, flock maintenance, or flock raiser feed.
Protein percentages should be 20% to 22%, especially while growing, molting, or in cold weather.
Once they’re adults and if they aren’t molting they can do well on a 17% protein feed in the summer/warm months.
Laying females require more calcium and protein, so a layer feed is appropriate, or mixing one with a all flock, or by adding eggshells or oyster shells free choice if they’re only given an all flock type feed.
Non laying females, juveniles, and ganders do not need extra calcium so feeding them layer feed can cause health issues eventually.
I feed mine Purina flock raiser year round with oystershell available in a separate bowl if they want it. It makes it fairly easy to feed a mixed flock of ages, genders, and even species.
Modern goose breeds are far larger and require far more than their ancestors, wild grey geese are tiny compared to their domestic descendants, Chinese geese are closer in size to their wild ancestor the swan goose, but even they are larger and need more feed. A wild goose could possibly survive on what a domestic duck is fed, as long as they can also find a source of calcium when laying, or algae for various vitamins, including the Bs, but domestic geese just are too big for that.