"The rat king is mostly, if not entirely, made of rats" = "If the rat king is not made entirely of rats, than it is mostly rats."
I think it is entirely rats, but I am not sure enough to claim it as truth, but even if the absolute is not true, the next step down is.
As far as the shades of meaning/rhetorical reasons one would use this construction, the "if not" construction allows one to push their meaning towards something stronger than they are prepared to defend. This construction suggests that the stronger position is true, but keeps the speaker from having to defend it. "I know many studies are X, and I think it is most of them, but I am not prepared to back that up by having counted." "I think Abbott is moral toxic waste, but I don't want the the burden of the absolute by saying there definitely isn't even one small good part left." your reader/listener can't unread/hear the suggestion so it can strengthen your position, but you haven't actually claimed it, so you only have to defend the weaker claim. It is frequently used with the second statement which is an absolute (all, every, entirely, etc.) Absolutes are easy to disprove, you only need to find one good moral position Abbot has, or one mouse in the rat king... In the case of "many, if not most" it is the same idea. "many" is a vague claim but "most" has a fixed meaning (>50%) and so is easier to disprove. There is no clear way to disprove "many" and so it is a safer position to take.