Regular vets who aren’t avian specialists really can’t do much for pet birds aside from mending injuries; an avian specialist can help you diagnose diet issues before the bird is critically ill, so it might still be worth taking in a bird that seems a bit under the weather to see if it is a diet issue - an awful lot of pet bird problems are diet issues. I took mine to one to have a microchip implanted before exporting her to Germany; not a huge deal with big parrots (they can be injected into the wing), but for small conures, it involves general anesthesia, so I went out of my way to find someone who had a lot of avian experience.

But yes, once a pet bird appears seriously ill, it’s likely too late to do anything other than keep it warm and in a place it feels safe, and let nature take its course.

As far as I know, pretty much all animals, especially prey animals, hide illnesses and injuries, and that is definitely the case for parrots.