Every dog is going to be different (obviously) but to have the best chance you definitely want to look at the breed's heritage.
Avoid any terriers. They were typically bred for hunting and killing small animals.
Avoid sport/hunting breeds (retrievers, hounds, spaniels, etc) because they were obviously bred for hunting and birding.
I would say to be very cautious of herding breeds, but aussie and corgis are both herders and it seems to have worked for you so far.
Herders ideally shouldn't have much drive to KILL small animals but part of herding is nipping and basically terrorizing the herd into obeying them. Could be a bad instinct to have and cause accidents.
Livestock guardians can be good because they've been bred for a very long time to watch and protect flocks and herds, definitely not nip, chase or kill them. But even some LGDs have been known to kill chickens.
With corgis, you also have the benefit of the short legs so as long as your birds are caged they are safer.
Edit: my dog is mostly pyranees, a livestock guardian breed, and he is very calm around the birds. I still never let them out at the same time - but he clearly just considers them part of the family rather than something he wants to yet at.