Budgies are omnivores which means they are perfectly capable of digesting both vegetables and insects. In their natural habitat in the Land Down Under, they have a varied diet based on grass seeds, leaves, insects, and other similar things generously offered by the Australian continent.
While this isn’t a true option for a domesticated bird, a good owner will still try and stay as close to this diet as possible. A tamed budgie keeps its main characteristic when out in the wild and it is an extremely curious and active bird that will try and eat pretty much anything you offer it. Therefore, you’ll be responsible for what your bird puts in its mouth.
As a side note here, these cute birds qualify as omnivores because they are able to digest insects. For the love of all that’s good, do not offer them a slice of steak or other types of meat. No milk as well since their little stomachs can’t handle it.