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Under normal circumstances, when properly holding a budgie and using a safe grip, it's not normal for the budgie to lose so many body feathers in the process and this is even when the budgie is being squirmish and tries to break free.
When budgies feel threatened they can fully release their tail feathers, but this wouldn't affect the body feathers on the rump area and above it like is the case with your budgie.
Despite the loss of feathers in that specific area, your budgie should be fine and will not suffer from being cold.
In 2 - 3 weeks time you should see signs of feather growth in the area.
If you don't notice any growth and she starts to lose more feathers, then booking her an appointment at the avian vet specialist for a full examination would be the best course of action.
It would also be best to refrain from holding your budgie and to reinforce the finger taming while inside the cage so that the next time you allow your budgie out of cage time you will be able to take her back inside the cage by offering your finger or perch.