tbh i think it’s less about shippers and more about aang being emotionally repressed at the beginning due to his intense feelings of survivor’s guilt and loneliness. keep in mind that he’s not touchy-feely with the rest of the gaang, even though they are with him.
once he finally forgives himself for what happened, he initiates their last handhold and reaffirms how important katara is to him. we see him revert back to his cheerful, goofy self. throughout the credits he’s laughing and spending time with the gaang, entertaining them and being the center of their attention.
i’ve no doubt that if we get future adult gaang projects, aang will go back to being clingy.