As
@CountryMage, as well as one other, have said or implied, MC doesn't want credit for everything or nearly anything he has done. He has the typical Japanese mindset of keeping a low profile because fame is embarrassing (it's not
exactly that, but close enough for argument sake). Because of this literally the only people who know about the things that he is capable of are those who were there at the time and those he is incapable of not keeping it a secret from (i.e. the queen, his father, and very few others). This is because he requests or outright
tells them to keep it a secret (through various means, including saying someone else did it).
Because the queen is in on the secret and has agreed to keep it so the other high ranking nobility that do know are required to keep their mouths shut.
@NextOrder points this out. You later respond that "his entire family is high ranking nobility" but that is wrong. His father is nobility (as is his mother, but I can't remember if she's still alive, and for the purpose of this it doesn't matter), the children
are not. They are "children of high ranking nobility," which isn't sophistry or "the same," because the "child of a noble" inherits the nobility of the parent (when they die or retire) OR
earns their
own nobility separately.
Regardless of being the "heir apparent" (meaning "one assumed to become the heir") the elder brother is
not the noble that his father is, and won't become it until his father dies (and he is declared the heir) or retires (and the same), otherwise the brother would have to earn his noble "title" independently, as the MC would/could have if he didn't outright reject the honor he has earned to this point.
All this is to say that without acting directly along side his father, his brother has no circumstance to learn who the MC truly is because the MC is doing absolutely everything to prevent his fame from spreading (with the two exceptions of "continuing to act" and "being presented at his pharmacy").
It isn't a vacuum, but there are things actively preventing the brother from learning the truth, similar to, but in a vastly greater scale that, what his brother and brother's friend are doing about the brother's disease...