Still sending you and your family positive energy and hoping your bird makes his way home. I don't know where you live, but I'm in Pennsylvania and pet birds are found outside all the time, probably because they stand out like a sore thumb here, regardless of the season. They sound completely different than wild birds and obviously look completely different than most wild birds here, and it seems in my rescue experience that most pet birds (tame, friendly ones anyway) that get lost outside typically become hungry, tired, etc. after a couple of days, and then someone sees them and tries to get them to come to them, and the bird eventually does come to someone. I've actually seen 3 specific cases that I can think of, maybe more that I don't remember, that a lost parrot purposely walked right up to someone that they saw outside, like they were asking for help. In all 3 of those cases the person that found the bird brought them in to a shelter or veterinarian and they called the rescue and brought them in. 2 of those birds, a blue and gold macaw and a cockatiel, were recognized by us at the rescue because their owners had called us to report the bird lost. So the birds went to a person who they saw outside, were taken to the rescue, and reunited with their owners all on the same day. I don't recall how long those 2 birds were missing but they were both missing for at least a couple of weeks. The third bird was a peach-faced lovebird and we kept him for at least 3 months, advertising that he had been found from day one everywhere we could advertise it, on the local news stations, local newspapers, websites, at all the local shelters, veterinarian offices (I've seen tons of dogs and cats reunited with their owners because their owners notified all the local veterinary offices that they were missing, and the authorities typically call or stop by all the local veterinary offices when a pet is found), and no one claimed him, so after 3 months we adopted him out. But the point is that the system does work, and lost birds are found after missing for days, weeks, months, and in a few well-known cases they were reunited with their owners after missing for years. So you'll get him back, I know it.
"Dance like nobody's watching..."