Pococok
I use a budgie mix of canary reed grass seed, millets (2 or 3 types typically in budgie mixes), and oat groats for my finches as well as my budgies. No dried fruit bits or pellets, just the seed.
But as Icearstorm says, we also feed lots of veggies, hopefully making up about 80% of their diet. I no longer feed any spinach due to its high oxalic acid content which I believe was the main factor that caused a hen of mine to succumb to egg-binding. They did love their spinach - but they now love their baby kale and arugula. I feed a "Spring salad mix" which is kale, brussel sprouts, chicory, and broccoli strands, and add some baby kale and arugula to that. They used to go nuts for broccoli flowerets but now ignore it.
Do not feed avocado, it is deadly to caged birds. Also mushrooms. Stick to green leafy veggies, and chopped carrots, sweet potatoes, and/or cauliflower. Google "Bird safe vegetables" for a longer list.
I also feed CeDe dry egg food because they won't eat actual mashed up boiled eggs. For vitamins and mineral supplements, I use Oasis Vita Drops in their water (their only source of Vitamin D3) and ABBA mineral mix. Other sources of calcium include a cuttlebone, a mineral block that is scored and/or has the edges knocked off (otherwise too hard for finchly beaks) and crushed egg shell in a treat cup.
I make a bird bread now that is corn-free. It has a ton of veggies in it - sometimes I over-buy the fresh veggies and turning them into bird bread is a very effective way to use up a salad mix that's getting close to the end of its usefulness.
My wild finches love sunflower leaves. I'd like to see if my caged guys like it as well this summer, assuming I manage to get any planted.