I think all of mine have been pretty good foragers. I've had a lot of different breeds, but mostly heavy weight breeds the last 20 years. They range all over and will cover 5 acres, depending on which gates are open.
Mine seem to forage farther, sooner, if they have someone or something to follow, especially to new areas that they aren't sure are safe. I've had them follow sheep they were pastured with, other chickens or me when I've taken young ones out foraging to new areas where I want them. One year I had young pullets that followed one of my cats around when they first started foraging. They love to follow fence lines, buildings or hedges, too. The fence lines are really tempting here, because of the leaf litter along them, that has tasty insects and worms underneath. The sheep always loved browsing up in the woods and the chickens love the leaf litter there, of course.
They seem to prefer what they can forage over what's in the feeder. They still like the grass, pasture legumes, leafy greens and seeds in the fall and early winter, but really miss the insects, larvae and worms. They also love to forage on different berries and fruits in the growing season. They spend more time in different parts of the property, depending on what's available at any one time.
I think foraging is an instinct, but it's also a skill that chickens learn. They have to learn where it's safe to go, what is safe to eat and what is good to eat. Over time, as they mature, I see them get better at it. I see my more confident, bolder chickens are willing to take more risk and flocks that have at least one risk taker can follow their lead. I do think brooder chicks are at a disadvantage compared to broody/flock raised chicks, if they're left on their own.