What Kayla said, but some birds do go outside into an aviary in the day time, the ones that she showed you were the Womach's aviaries in their garden for their macaws and toucan that they go into during the day, but they're indoors on a night, they're also not exactly HUGE aviaries so they wouldn't make good permanent homes, those ones are more... outdoor cages to be honest
When I think of an aviary I think of something that is either made from metal or wood with metal mesh (or plastic in the case of birds of prey) that you can make pretty large. You can build to size, I used to keep many budgies outdoors, they had an indoor/outdoor aviary which was 15 foot long, 7 high and 4 wide. Then I had one next to that which was 6 foot long by 6 foot wide by 6 foot tall, and that had holes in a wall so the budgies could run inside and go into their breeding cages. It worked really well
The weather in England is bipolar, honestly. For us, one day it could be horrific rain the next sunny and the next snowing. Our birds cope well in this weather, well most do anyways. My kakarikis love it!
Typically an aviary bird would be something that may be just for show, like look but not touch, or perhaps breeding. However, Pickles my green cheek x maroon bellied conure was bred in an aviary, raised in an aviary with no human contact yet he's probably my tamest bird, regardless of the others being hand raised! It all depends on the bird but perhaps if you did want rosellas it would be best to get a pair
I do think getting the budgies from rescues etc to have them in an aviary is a lovely idea