I free feed. The feeder is elevated to prevent scratching food out. It also has those spokes in the tray, to prevent billing out. So, wasted feed hasn't been a big problem. We also don't mix anything like scratch into the feed, so they aren't picking through it, looking for some better bits. Other foods are fed separately from the commercial feed. I don't know if any of that would help with your food waste problem. Some people also feed two meals a day, after chickens are done growing.
My chickens get better at foraging the more experience they have with it. Foraging is a natural instinct, but it's also a learned skill. In an established flock, the chicks learn this from their mother and the other chickens in the flock. Chicks raised in a brooder have to learn by trial and error, unless you help them. Bolder, more confident chicks take more risks than shyer chicks.
Part of it is that they need to experiment, to see what is good and what is safe to eat. They only way to learn that is for at least one of them to be brave enough to try something. The more foods they try and like, the more they'll be encouraged to try.
The other part is that they're frightened in new environments, being prey that is eaten by so many predators. Chickens normally stay closer to the coop when they first start free ranging and go farther away as they gain confidence. If they don't have any cover and are exposed in an open area, they're more fearful than if they have cover, like shrubs or some type of man-made structure that they can take cover under.
I take chicks out as soon as the daytime temperatures are similar to the brooder temperature. I get them on grass and let them run around and nibble in a protected area. I have a grow-out chicken tractor now, but before that I used a patio table with hardware cloth wrapped around it and just watched over them. It gets them used to the outdoors and the property early.
When they're older and a little larger, I start free ranging them. I take them for walks. With me standing around with them, they feel safe enough to come out of their enclosure and start wandering around. Even doing this just once or twice seems to really help. Once they've visited different areas, they get more comfortable there.
My property has particular areas that are good for foraging and I take the chickens there. I turn over the leaf litter to expose insects. I show them the pile of insects under the bug zapper. I take them over to the area with dark leafy greens growing. You can toss some bits of seed or grain lightly in an area, to start them foraging in a new area, too.
If there's a particular area you want them to spend time foraging in, try walking them over there. Toss a little seed or grain over there, to get them started. If your chickens don't naturally follow you as you walk over there, try scattering a bit of seed or grain as you go. The basic bread crumb trail method usually works.
You might want to think about different foods you could plant for them, too. Legumes help with protein, as do insects and worms. There are lots of threads about this.
