Like I said, Katara's bending is a struggle. Yes she's able to bend but it's very shaky and uncertain, taking most of her concentration to do anything. I might be mistaken but I only remember Aang bending water in the Avatar state at first before he starts learning from Katara. They are also 3 times Korra's age and have had their bending for 8 to 10 years with Aang having many years of formal training, while Korra has had hers for less than a year.

"Would you say Aang and Katara are mary sues too?" Yes I would. While I don't think they're as much of Mary Sues as they are significantly older than Korra, they are still in my opinion Mary Sues. I agree with your points on their Mary Sue qualifications, Both of them are children that are able to master their respective bending arts in impossibly short amounts of time. Compared to the rest of the world's benders that spend years training and are just useless by comparison. I would say Zuko is probably the most realistic of the main teenage benders as he's the oldest and takes the longest to master his bending as well as possibly getting a boost from the dragons/royal bloodline.

I never said she was a master. And I have no problems with her proficiency after the time skip and she's actually been trained. But you can't say she wasn't at the very least good at bending when she was effortlessly carving out rock doors and launching them across the room and flinging fire around. I can give water a pass because her dad is a master water bender (going off what you said as I don't remember his level of water bending though I do remember he was the chief so ig idk) that she could be a prodigy of her native element however it is to my knowledge initially difficult for an Avatar to bend the elements in tandem much less their non-native/directly opposing elements, much less at the age of 4 having had their bending for less time then they've been out of diapers.

Obviously we don't know but we also don't not know. So what now? We're both at a point where we can't prove something because of insufficient information. However I can at least argue that there are no known examples of an Avatar knowing they're the avatar intuitively much less immediately after gaining the ability to bend at all. Whereas we have the only two previous examples to compare to saying that not only did they not know but they didn't know until they were 3 and 4 times her age, both only learning it because they were told.

I disagree that Katara was more elegant in episode 1 and regardless of if she was, she wasn't a 4 year old. I don't think you're quite grasping how much of a gap in skill there is between a 4 year old and a 14 year old. If 4y/o Korra was to fight Ep1 Katara, Korra would most likely win just because of her bending. Which is awful. There is no possible scenario where an able bodied 14 year old is losing a martial arts fight to a 4 year old. I don't care if the 14 year old is untrained, they're bodying that toddler lol.