I'm going to comment on this as a native speaker. It is not a commonly used structure in everyday spoken English. You would find this used more often in advanced books. Basically the "all the less" phrase means a strong version of "less", such as barely doing something, or strong dislike. The "so as" connects the feeling to the reason why. So, for example: The girl smiled all the less so as not to alert her admirer. Here the girl is smiling, but a lot less because her admirer is there and she does not want him to know that she likes him. It gives more detail in written language than just saying "The girl smiled a little". It is a fancy way of describing details in written English that are often expressed in context and gesture/facial expression in spoken English. You will also see "all the more so as" in many books as well.

I don't know what exactly your book said but to me "all the less so as" seems to be not the best way to approach it. The commonly seen phrases are "(all) the more so" and less frequently "(all) the less so" (24.8M vs 373K on google). In other words, "as" is not part of the phrase, and even "all" is not essential but just adds emphasis. These phrases usually need a reason, so is often followed by "because", "as", or other similar phrases. "all the less so as" with "as" is just a very rare special case of this pattern. As for the meaning and usage, "so" is referring to what was already said before (again, not part of "so as ..."). So we often see phrases like this: - Success seem hardly within reach - all the less so because his funds have now been reduced in half. - He was ecstatic, all the more so now that he has his family's backing. You see that you don't need the "so" in these examples. And here's a take on it at merriam-webster.com. Definition of (all) the more so —used to say why something (such as an attribute or quality) applies to a greater degree or extent <The play was impressive—(all) the more so because the students had written it themselves.>