Could she learn something by using Christa's telepathy on the dragon? Unlikely, but likely not particularly risky if there's that much traffic involved. There is the potential problem of Yui recognizing her scent and things somehow going wrong from there.
The late hours of a Dragoon functionary provides some new information, but that could easily be a response to either the Red Queen or Alard's imprisonment. It doesn't, she think, give her much more actionable information, as something similar was predictable in advance.
Wait. She's been an idiot. She should ask Jasmine if faking Christa's murder by Alard sounds like something Rele would do. And surely others knew Rele to some degree, she should ask them as well.
She needs to adjust to her new cult being valuable not just as additional hands, eyes, and ears, but also as additional minds.
Somehow, thinking about the questions she should ask helps her feel out what she thinks her own answers should be, hinting to her that she was over-anchored on her original idea that the Lord-Commander was responsible. But she goes through with asking her questions anyway.
So, she telepathically asks Jasmine who knew Rele or the situation in the city at least somewhat well. And then, she can go one by one and ask each individual a few questions telepathically, to avoid any answer biasing any of the others. Does something like Alard's false murder of Christa look more like an odd move by the Lord-Commander against a Christa that he thinks killed one of his agents, or Rele frantically attempting to cover for an absent Christa and erring in determining the amount of attention such a thing would bring? And what, in their opinions, are the most likely things to have detained Rele?
The value of the answers she gets depends on how well-known Rele's personality is in the cult, and how well-informed the cult is on the city in general and the Lord-Commander in specific. How does all that shake out?