I think she pretty much assured all of us that he/she is on the mend. And give her some credit please, I doubt she would allow the bird to suffer.
And after leaving my cats to die in the hands of veterinarians, some under very mystery circumstances, (one was butchered) I do not share the same enthusiasm you do towards vets. They are not always the 'be all or end all' when it comes to treating sick animals.
Budgies are notorious for hiding symptoms, and just being on the mend now doesn't mean much in the grand scheme of things. Ciri was showing massive improvements too, before she suddenly passed away, even after getting a proper diagnosis and care. My lovie was starting to use his foot before it suddenly shriveled up and fell off. They're very delicate birds, denying them medical care is likely a death sentence. At least if this bird gets to a vet, it might have a chance to survive.
I'm sorry about what happened to your cats, but that doesn't mean all vets are like that. She might not even have to leave her bird overnight. Vets are the only people who can properly diagnose and treat sick animals, afaik.
Your experiences, as sad and heartbreaking as they are, still don't mean this budgie doesn't need help. Again, I'm really very sorry that happened to you. What happened wasn't right at all, and it wasn't your fault in the slightest.
I've had a lot of positive experiences with the vet myself. The vets I've been to have been kind and taken the best care of my animals as they could, even steering me away from risky procedures that would have killed my bird but made them a lot of money. There was even a time my mom couldn't afford to get one of our old dogs treated with life-saving surgery, and me and my brothers convinced her to let us pay for it out of our frozen school accounts. There was a waiting period before we were able to withdraw and provide the money, and the vet was willing to see him right away and be paid later. He would have likely died if we waited the two weeks, and the vet had no way to assure we'd pay. (Which we did, in full).
Not every vet is like the horrible people you encountered.