The sentence is taken from the 4th volume of 『裏バイト』
Context: A son whose mother is a successful designer has returned home for the first time in 10 years. His main reason for leaving his parents was that he aspired to become a designer on his own and ultimately wanted to become more successful than his mother. While listing some of the realisations he made during this time he ends with this sentence.
My question is regarding the 「如何に～か」construction. Initially I wondered about why a 「か」stands at the end of this sentence, and while searching the Internet for a bit I came across this article:
From what I understand the 「如何に～か」is regarded a construction on its own here. Generally speaking this construction seems to be used to underline that “the extent of something is large/high/etc.” What is underlined is placed between 「如何に」and「か」; therefore in the example sentence it is used to understand just how high his mother’s design skills are, right?
Anyway, I was not able to find any other explanations of this construction, so I am still a bit unsure about whether my understanding here is correct or not. I am not really able to explain why, but dropping the「か」sound weird to me. So it might also be the case that 「如何に～か」is not a construction on its own, but rather that 「か」 is necessary in phrases like these (for grammatical reasons I don’t seem to understand). If that is the case, why is this necessary?