I never owned a bird but I strongly do not suggest putting her down.
I am sure there is a possibility she can be saved. If you ever watch VetRanch's YouTube channel, they get so many cats and dogs that were supposed to get put down or euthanized but VetRanch has veterinarians that actually save the animals' lives.
My girlfriend put her rabbit down and she regrets it. It was midnight like 12am or later. The only animal clinic opened wanted to charge us $800 USD to send her rabbit to the hospital for treatment. We did not have that money.
We brought the rabbit back to her house to discuss while she was crying and balling her eyes out. In the end, she decided to put her down. I had to leave at that time because I had work in the morning and it was late already. She said the clinic took her rabbit in the back and euthanized her. That's all I remember her telling me. It was sad.
She felt she killed her own animal. As much as people like to think euthanization is always a humane way to out an animal down, I do not agree that's always the case. Her rabbit was attached to my girlfriend. Imagine the rabbit seeing an unknown person being carried away from her owner into an unknown room and euthanized, then slowly dying.
My girlfriend felt that she could have waited over night until the usual clinic she goes to opens up because there was a very good rabbit veterinarian who could have possibly saved her.
She even said if she could not make it, she rather have her rabbit bring her back home where the rabbit is familiar with the area and not some strange animal clinic that the rabbit is unsure of and may feel distress. She felt the rabbit should have passed away in the comfort of being by my girlfriend's side in the home where the rabbit was raised. Animals prefer known areas. That's their territory and their home. They feel comfortable in these areas.
If you were dying, would you prefer to die in a hospital bed or in the comfort of your own home?
I am not against euthanization but it really depends how much pain and what condition the animal is in. So please reconsj your options.