I'm so sorry for your loss of Budgie. It sounded like she knew she was in a good place even for the short time she was with you.
Sometimes, sudden deaths happen, and it seems she may have had a pre-existing condition before you got her, or went through a sudden seizure, heart attack, or stroke.
Please don't blame yourself, you did everything you could for your little one and she had the best few weeks of her life with you and your family.
Budgie is now over the Rainbow Bridge, looking down on you fondly. May she perch in your heart forever even though she wasn't with you nearly long enough.
My heart goes out to you for this sudden loss. I hope that after your grief passes you will be willing to take in another little budgie and show them your love just like you did for your little one.
Rest in peace and fly high, little Budgie. Best wishes to all of you.