I just want to add that, having worked with falcons, hawks, and eagles in the real world, the idea of "barding" a bird is a non-starter. We make backpacks and foot attachments for small electronics payloads, but these things weigh grams. Adding any amount of wood/bone/leather/metal that provides protection from weapons would make any bird so heavy that they would not be able to fly, or could only fly for very short periods without getting tired. Eagles are pretty lazy as it is, and won't work hard to fly.

Of course this is fantasy RPG, so by all means, if you want full plate barding for your hawk familiar/animal companion, go right ahead. It's just something that breaks the suspension of disbelief for me.

Magical protection is much more workable.