Some historical context for this chapter from a tiny bit of digging.
We know it's about 1520 as Leonardo Da Vinci's death was mentioned in chapter 38.
Cardinal Silvio Passerini was a Medici loyalist and Cardinal in Florence at around this time.
https://en.wikipedia.org/wiki/Silvio_Passerini
The "Mad Queen" is likely Joanna of Castille. Queen of Spain (as a unified Aragon and Castille as the daughter of Ferdinand and Isabella) and Naples (Basically southern Italy as it was under personal union at the time). She purportedly went mad after her husband died and was imprisoned for decades by her son Charles I (Also Charles V of the HRE) until her death in 1555.
https://en.wikipedia.org/wiki/Joanna_of_Castile
Considering she refers to others as "these adults" and judging by the use of the nickname Irene, the traveling noble is likely Joanna's daughter Catherine (Catherine -> Erine -> Irene I know it's flimsy but of Joanna's daughters she fits the best) There's no record of any of Joanna's daughters going on prolonged diplomatic trips in their youth, at least not from a quick glance, but Catherine is the only of Joanna's daughters that would have been unmarried at the time and thus able to make a trip like this. Furthermore she fits the perceived age of the character (14-15 )and was known for gathering Female scholars as courtiers later in life during her time as queen of Portugal, which would fit in with Arte's themes.
https://en.wikipedia.org/wiki/Catherine_of_Austria,_Queen_of_Portugal
So yeah, she would be an appropriately "big fish" to elicit such a response from the cardinal. You normally wouldn't have a Hapsburg showing up in your parts in the 1500s unless something was getting inherited or there was some inbreeding to do. It's nice to see the author pull figures more directly from history.