Most of us were forced to read 1984 and didn't really enjoy it. ATLA however, is something that we organically grew up with through high-school / college and actually paid attention to.
My group of friends would be aware of 1984 concepts... such as "Big Brother is Watching" (phrases / concepts which have escaped the book and become a thing of their own). But I don't think we'd recognize the phrase "At War with Eurasia".
Honestly, the only reason why I remember "At War with Eurasia" is because I was a quiz-bowl player and was forced to memorize key phrases from many books I barely read. Even if I did read 1984 in my high school classes, it never actually stuck with me.
1984 is a very popular and influential book.
I fairly confident that if you asked the authors of Avatar The Last Airbender they would tell you straight that they’d based that idea on 1984.
I’d be willing to bet people will be quoting 1984 long after ATLA has been forgotten.
The original two posters in this thread were also intimately familiar with Ba Sing Se / Avatar the Last Airbender. So multiple people here are fully aware of the reference and are in good communication.
I probably wouldn't reach for a reference to ATLA myself. But, apparently its popular enough that plenty of different posters in this very discussion are aware of it and able to explain to other people here the concept.
I'm your age and I never even heard of Avatar the Last Airbender. I'm sure my younger cousins know about it.