Realistically the Heights are also rife with magic auras. Nobles and students playing with illusions to change their appearances for whatever reason, everyone glimmering with magic items. I'm only going by the same line of thinking that leads to the crazy security measures around the theatre.

So even with detect magic in the Heights at least its still a case of being lost in a crowd. It should take some close scrutiny to figure things out especially with Dalen and Aliani on hand.

Also the conspirators probably have limited resources at the moment and are trying to be low key in capturing Trinia at least until word gets out about the king and they can frame things in the right way to publicly go after her. I don't know how much of this part we can put together or if this is more meta-thinking.