Yeah it's a filler episode, I won't disagree, but that's a pretty standard thing with series shows. Not every episode needs to push the main plot. Sometimes you need a break to flesh out interpersonal relationships, establish some backstory for a character, or just have something fun before you go into a really dark 3 parter where everything is pain, misery and betrayal.My main problem with the painted Lady is basically just that. It's already been established that Katara is a caring person and continues to grow. There is also Katara's my way or the highway attitude. I did not like it. This is where everyone's complaints about her being a busy body or nosy really comes into play, or other anti-Katara fans get their sources from. The problem is that later episodes do it better and a coincide with her character and development, and the plot. My problem is that the episode felt like it's something that should have been done in only season one, or early season two. The concept of design of the painted Lady is awesome, but I felt it could have been used for better effect elsewhere. The episode is filler you can skip and you literally would not miss anything. But if you enjoy it, more power to you.
As to her being established as a caregiver before, I dunno, for me, prior to painted lady, it was usually framed as her being a "nagging mom" kind of character. that she cared for people because she felt they needed someone guiding them. Not just that it was a part of her nature, that she was someone who wanted to help others, as her fundamental being. Not just because she felt sorry for this little bald kid, or her bumbling brother, but because that's just what she wanted to do with her life. To spend her time helping others. So to tell her to not do it, was something that went against the very core of her being. So she refused. She could help, so she WOULD help.