I've been thinking about this too, for when Mr Theo passes, I know I will never be without a dog. My lgd breeds and Danes surprised me the most. The Anatolian and the akbash have saved more lives and money than I care to count, including the birds, cats, whatever is part of their herd. The Anatolian once laid down by an injured wild turkey (his alert was to stay with whatever trouble he found until a human relieved him) until I got to it... Same with a goat in a well once. Their drive is reserved for predators, and even try their best to scare away hawks. Both the lgds and the Dane physically brought baby animals to me. The Dane scooped up a Guinea keet, the lgds carried lost goat kids home after waiting over 24 hours for us to find them.
I'm not saying that a close interaction is safe at all. I'm just pointing out that there are breeds whose job it is to keep a herd (which is not a specific linear thing, and can include many species) in tact and defended at any risk to themselves. Even the guardians require reasonable respect for their personal space and food. A swift jerk of the head can result in unintentional injury or death, a playful paw, etc...they are massive.
Any dog you choose will be a threat to your bird, regardless of their intention. Try not to choose any breed with a high prey drive.