Please do all of the above.
Companion birds have companion humans. If your bird is having a rough time he will seek out bird feeders, bond with a flock of something or look for a human to take care of him. Write up notes to put on doors so you can pass the word even if the people are not home.
Spread the word by FB also. There is a parrot group on there that has been working together to find lost birds. There was a woman who had to go to the hospital and left her bird to be cared for by her brother. He sold it and used the money for drugs. He could not remember who he sold it to. The woman was devastated like most every Parront would be. It was quite a few months but this group found it and had the police claim it for her. It was still in the same state but counties away from her.
Your bird may already have been taken in. Not everyone will try to find it's home. A reward might cause a neighbor to tell on a neighbor with a found bird. Tell the kids in your neighborhood. Ask them to spread the word in school. Post a reward in schools also. Kids will search for it in hopes of a cash reward.
Wolf's first bird was one that found him and would not go away. The bird somehow got loose, flew around and had fun but got lost. When he could not find enough food he found Wolf.
This is all very time consuming. Your thoughts are consumed by your fear for your bird it does not make much difference.
My belief: Pray ! I believe in miracles. When your bird is found remember to praise the LORD for it.
Check with bird feeder people. Ask them to watch for your bird at their feeder.