I think from a story standpoint it is very difficult. I think they do need to be careful how the character comes across because yeah many people would take it as her being catty to her friend. I get it.
But they also have to show the character has feelings for Cloud as it's part of her story arc. She sees him as more than a friend so I think they decided flirting would be the way to show that. Like they need to show the audience she falls for him somehow.
It would also be weird if the character didn't show rising affection towards Cloud considering players are given the choice to raise her affection in the game. Like no point in having that affection point system if her relationship with him feels like the same friendship as everyone else.
With OG it was more extreme bc it was polygon people with faces that looked like this
So you gotta exaggerate to get the point across. Then they had Tifa on screen to show this polygon had feelings too for the same guy.
Here the interactions feel more natural. In HD we can see all the characters interact subtly.
I do wonder if they could have showed Aerith's feelings for Cloud and her being torn over him and Zack another way. Like maybe showing her fall for him secretly anime style away from Tifa. Maybe looking at him from a distance. But with her forthcoming and bold personality I'm not sure how well that would work out.