Katara has definitely spread herself thin on the ship: she loves the GAang, but knows by now that they can handle themselves and have lives of their own. Some people don't and some people are just different friends she's met that she cares about too.

And yeah, she's gotten bad at that, even though she tells them with the best intentions in mind. She actually considers people like Alex and Eva brave after all they've been through and thinks others should too.

The Azula thing she's not telling anyone and wants to keep it that way. While she'll freely tell the Hama story, what happened with Azula's breakdown is far too dark, even for her.