Lies of P thoughts, contains spoilers
I feel like Lies of P (shortened to LoP for this) is probably one of the more interesting popular/big budget adaptations of the original serialization, at least compared to Disney's, which alters the story from being commentary on the obligations of vulgar Italians during the Risorgimento in a growing industrial world to being one about external paranoia. Obviously, because it's Disney and in the 1940s where Americans were experiencing exceptionalism and external paranoia, as well as the increased reverence for the Nuclear Family, the agenda behind the messaging is pretty evident.
But LoP doesn't maintain any of these messages, because P is awakened into a post-industrial and plague-ridden Krat, and the people that P comes to rely on is not his family/creator but instead the people who he has been introduced to through his travels (for the most part; "Alidoro"/Parrot has been lying about himself the whole time). There is no obligation for P to get over himself and assimilate into a rigid structure to provide for anybody, because this is a post-structural world and he never feels the original Pinocchio's struggle between what he wants to do and what he's supposed to do—P is always doing what he is supposed to do and is equipped to be able to tackle every obstacle in his way. He never goofs off or does silly things or is lazy, he never smashes Jiminy with a hammer for being annoying, and he never goes to Pleasure Island with Romeo/Lampwick. Even Romeo dies in LoP not from overwork as a result of his excess, but because P kills him (arguably, Romeo is already dead and P has killed his reanimated corpse, foreshadowing a potential ending) because he is told to.
I would argue instead that LoP is an inverse of the original Pinocchio, naturally as a product of its context. P's ascension to humanity is indicated physically (your "gears are shifting", for example) when P opts to lie and to exercise choice in this manner. There are other puppets who experience humanity, like Polendina, but these come from an awareness of emotion rather than choice, because even Polendina asks P (and by extension, you, the player) to make difficult choices on his behalf.
This option for choice and deception as a marker of humanity, while pretty individualistic, I think is attempting to subvert the expectations of being a puppet or a robot or a cog in the grander machine; it is a frustration with being an element in a capitalist world where things are fixed and one is obligated to do as they are told. After all, most, if not all, of the puppets P kills, aside from Romeo, are puppets that exist in a position of servitude, where the working class is quite literally stripped of its humanity.
In short, I think that P's ascension to humanity comes from his choice and his proximity to disobedience through lying. The less that P acts like a puppet, by doing things that are kind to others but might not necessarily be "true" or deviate from his goal as instructed by others, the more he is able to become a human, and that is only done through the insertion of the player's own human will.