I have brought parrots back and forth many times between Saudi Arabia and Canada. I would bring them with me for my summers in Canada. When I finally moved to the US, I brought the birds with me to the US Virgin Islands. It can be really problematic to import birds into the US, that is for sure. If I had brought my birds directly to the US, they would have required a 3-month quarantine in a private quarantine facility. If someone else's birds get sick in the quarantine facility, your healthy birds could be euthanized at worst or their quarantine period started all over again from Day 1 once the sick birds were no longer sick.
There is no quarantine for pet parrots between Canada and the US. I don't know about poultry, but I doubt they need to be quarantined unless there are current outbreaks of disease like New Castle (which would stop any cross border travel). There is a quarantine of pet parrots between Europe and the US.
Canada might be the way to go to import those birds. I quarantined my pet parrots right at my cottage in Canada. I had the Federal vet come out to approve the facility (something like $300). I had import fees and I think I had I a fee for the Federal vet to come and check on my birds during or at the end of the quarantine. All told I think it was around $600 to import my parrots into Canada. Once they clear quarantine in Canada, they are Canadian birds and the rules of transporting birds across the US/Canadian border apply.
If you are interested to investigate bringing birds into Canada, go to the Canadian Federal Food Inspections web site. I just did a quick check, and no birds are allowed in from Indonesia because of HPAI (avian influenza), but there might be some latitude with "pet" birds.
I had a pet rabbit I wanted to bring back to Canada when I finally left Saudi Arabia, but it was impossible because of some endemic rabbit disease in Saudi Arabia. Fortunately, she found a wonderful home with a rabbit lover and lived to a ripe old age.
My luggage made quite the spectacle in the lineup to check in for my flight on my when leaving Saudi Arabia for the last time. All flights leave after midnight, so at about 1:00 a.m., I checked in with: Five old guinea pigs, four parrots, three humans (two kids and a husband) two cats, and one a mini Dachshund (dogs are illegal in Saudi Arabia except for guard dogs). two cats, four parrots, four guinea pigs. Sung to the tune of the 12 Days of Christmas, it was: Five (g)old(en) pigs, four calling birds, three French men, two Saudi cats, and a Dachshund under my seat.