TBF no one is looking out for a cross-dresser and nothing really sus has happened yet as Ikuto is too tomboyish which is kinda expected behaviour of a "boy". Pretty much, out of sight out of mind
This!
A huge amount of trivia:
His speech in the raws is super masculine (「俺」とか「できねー」とか「そうだろ」), too, albeit a bit childish at times (「ねーねー」). It probably wouldn't be easy for a pampered princess to fake that, so his past life is helping him to an extent, at the very least through creating cognitive dissonance.
The romaji for the Japanese mentioned above would be "Ore," "dekinee," and "sou daro." Any weeb worth their body pillows (jk) would know "ore" is hypermasc. The gender neutral counterparts for those would be, "Watashi," "dekimasen," and "sou desuyo." The fantasy fem version would probably be, "Atashi," "dekimasen," and "sou desho."
How a person speaks Japanese can say a lot about a given person, and unfortunately, it is often lost in translation, only acknowledged with passing lines about a runaway princess' change in speech.