That author seems to think soybeans are a kind of "grain." Almost everyone else says that soybeans are beans, not grains.you might find this useful
https://poultrynutri.com/feed/types-of-grains-used-in-chicken-feed/
If you leave out the soybeans, NONE of the grains have enough protein to be a complete diet for chickens. What protein they do have is short of certain amino acids.
So grains can be a good part of a chicken's diet, but cannot make a complete diet by themselves.
Adding soybeans can fix the total protein and the balance of amino acids.
By that point, you are starting to look quite a bit like purchased chicken feed (main ingredients are usually grains and soybeans), but usually at a higher price.
That would be why I suggested looking at chicken feed. If it is not available, or not at a good price, then it makes much more sense to consider buying single ingredients to supplement the chickens' diet. But for chickens that already "look terrible" and are being fed on scraps, I think a complete chicken feed would be a good starting point if it is available (and cheaper than buying human-grade grains and/or dried crickets.)