I'm glad you enjoyed the chapter!! 💖
About Yekbûn specifically, she and the Crown will have opportunities to deepen their relationship later, but it wasn't really the time for that in this chapter considering how busy the Crown is atm. The Crown's question about their parents is not about the Crown actually doubting that, it's more of a veiled way of saying, "can you reassure me about this?" especially after they feel the weight of expectation on them more heavily than ever. There's social nuance there ;)