^ By the way... I once re-homed a bird off Craigslist. Named him Newspaper. Bought from a real sketchy guy.. Smelled like paint, looked like he had acid paint stains on his skin, no toys in the cage. Paid him $45 for that bird, brought him home.
Bird had real thin feathers then started "twitching" and died 10 days later (from the day I got him.)
Reason I am sharing: OP, you are not a horrible Parakeet Dad. You do what you can. Sometimes, the bird is just sick.
Now don't get me started on the person that left my cat in the rain for three days (they had custody at their place at the time) and he died 6 weeks later............. Sometimes, it isn't your fault and these things happen.
I've been the one, had to check myself into an E.R. ready to commit suicide and distraight over loss of (said cat) so it's never easy, just know they are in a better place now. They are.
Sincerely, - Bonkers (this the name of a bird I donated to a friend, I had 14 birds at one point.)