Beyond echoing the design of Lady Loki, Sylvie’s broken crown on Disney+’s Loki series speaks to the character’s rough and tumble life. As a long-standing fugitive from the Time Variance Authority, her crown was likely broken in one of her many battles with its agents.
In Loki: Agent of Asgard, Marvel’s main Loki character also wore a broken crown, albeit for very different reasons.
https://www.cbr.com/how-loki-crown-broke-in-comics/