The bug
When untamed parrots take damage, they won't flee in panic.
This is inconsistent with other passive mobs.
Fixed in 22w18a for allays.
Linked issues
relates to 5
Attachments
Comments 9
Can also confirm

This seems to have been fixed for Allays specifically in 22w18a, as both tamed and untamed Allays will fee and panic after taking damage. This still applies to tamed and untamed parrots, however.

In 22w19a. Fix version 22w18a not 22w19a.

Unfortunately it seems now in 1.19 Pre-1, Allays do not panic when injured again. Should it be readded to this report or made into its own?

Please create a separate report for this.
In regards to the above two comments, the new report for that issue is MC-252078.
Due to the allay problem has been fixed, so delete the relevant screenshots.
Relates to MC-262561.
I can confirm this behavior.