@EaterOfBooks
Unless they have a system where they automatically 'elect' or place the currently X (some category, age, gender, skilled) person of the royal family to the next ruler after the former one dies, there's usually a lot more formalities to it, even if it's something as simple as 'I *name* hereby become the next ruler'. If they automatically do it, they still have to send someone out to inform both the people and the ruler that there's a new ruler, and said person doesn't really have any authority or status belonging to being a ruler before they've been notified and assumed the throne.
Otherwise they could just go 'The old ruler is dead. Long live the new ruler XX! But since they're not here, we'll be ruling as regent or regency council until they get here!', effectively usurping power without any legal basis to it, unless it's their traditional way of doing it , with a puppet monarch.
So yes, Sera might have the birthright to become the ruler, but until she decides to do it and does it, she's still just the princess if they have those titles (they might not have hereditary rule, meaning princess as a title might not be necessary or useful)