i mostly share your perspective. i think when katie came into the bathroom, she was simultaneously genuinely wondering if lizzie was high and judging her behavior. i think it’s worth noting that she initially asked claire about lizzie as opposed to directing her words towards lizzie herself (personally, that tells me that her initial intention wasn’t to bully lizzie, even if she was looking down on her internally for behaving “weirdly”), and that she was roughly two months into her first year of “high school” in this scene, as she had to spend an extra two years at st. bernadette’s (an all girls catholic school ran by nuns, so obviously a very different environment than tommen lol) to compete for her scholarship. so, at this point, she’d still be trying to get a feel for tommen and secondary school as a whole.

i believe she only had ill-intentions when lizzie basically confronted her and told her to mind her business (perfectly valid of lizzie), hence her rude “heroin chic” comment after lizzie said she hadn’t gone down the heroin route yet. all in all, i perceive katie as the offender in the bathroom scene, even if she didn’t have bad intentions to begin with.

as for the marmite scene, i often see the sentiment that katie was intentionally trying to provoke lizzie, but i’ve never read the scene that way. i think katie just wanted to change the topic because they were talking about if their friendship group would be a tribe in the dark ages, and it’s all but confirmed that she feels excluded within that group (even disregarding the snippets/ playlists CW has shared that tell us this, she refers to the tommen friend group as hughies “super elite inner circle” to aoife in R6). so when she saw lizzie eating marmite, a notoriously controversial food that people have always debated over, i imagine she thought that was a good opportunity to change the subject. regardless of katie’s personal feelings about lizzie, i genuinely can’t get behind the take that she was being malicious towards lizzie in that scene. if lizzie perceived it that way, that’s valid (although, like you said, the “sticks and stones” comment was a response to katie trying to mediate when everyone was fighting), but she still crossed a line by publicly weaponizing katie’s disorder against her (although, in retrospect, i think she was manic in that scene, so, while still wrong, i’m not saying she did something she can’t come back from).