Played the yue yan event and the only time she gets real offended is for your fang meddling other than that you can call her sovergien's lapdog and still only get -3 relationship,plus you can actually over-all have a net plus with the "apology" because yue yan also knows mc doesn't mean it and is only doing it for yue fang so you gain+4 relationship while meddling itself have -1 so yeah that is the only time she gets mad enough so it was more about family business and even there you can still have disagreement and still keep working.
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So yeah there is clear potential here as even on personal insults she doesn't call you anything only when you keep antagonising and pushing the yue fang issue lol and say you will stop her then while offending here well then anyone would start talking **** too just like irl people when angry start spouting things they wouldn't say normally at all.