My mum always has a crop of cress growing on her windowsill. They are so nutritious to add to sandwiches year round. I'm not sure whether all bird seeds are from species that grow edible plants, but the idea isn't impossible. From
microveggy I found this list:
Sunflower
White Millet
Red Millet
Canary Seed
Peanuts
Safflower
Nyjer
Corn
Milo
Of these only nyjer is not mentioned in pfaf as edible as leaves (although canary seed is basically grass!). They were talking about growing out the mature plants for feeding birds direct, which is a slightly different topic.
I think if I didn't know how the seeds were treated and what species they were, I would be fairly cautious about eating the sprouts personally. It's possible that different bird mixes have different seed content.
Other sources maybe commercial seed sources of leafy greens and brassica (you'll get more for your $) or (IMO) best is to grow out some of your microgreens to harvest your own seed for future greens if you have space (and the birds don't beat you to it!)